0 is the

additive identity.
1 is the

multiplicative identity.
2 is the only even

prime.
3 is the number of spatial dimensions we live in.

4 is the smallest number of colors sufficient to color all planar maps.

5 is the number of

Platonic solids.
6 is the smallest

perfect number.
7 is the smallest number of sides of a

regular polygon that is not constructible by straightedge and compass.
8 is the largest

cube in the Fibonacci sequence.
9 is the maximum number of

cubes that are needed to sum to any positive integer.
10 is the base of our number system.

11 is the largest known

multiplicative persistence.
12 is the smallest

abundant number.
13 is the number of

Archimedian solids.
14 is the smallest even number n with no solutions to

φ(m) = n.
15 is the smallest

composite number n with the property that there is only one group of order n.
16 is the only number of the form x

^{y} = y

^{x} with x and y being different

integers.
17 is the number of

wallpaper groups.
18 is the only positive number that is twice the sum of its digits.

19 is the maximum number of 4

^{th} powers needed to sum to any number.

20 is the number of

rooted trees with 6 vertices.
21 is the smallest number of distinct

squares needed to tile a square.
22 is the number of

partitions of 8.
23 is the smallest number of

integer-sided boxes that tile a box so that no two boxes share a common length.
24 is the largest number divisible by all numbers less than its

square root.
25 is the smallest

square that can be written as a sum of 2 positive squares.
26 is the only positive number to be directly between a

square and a cube.
27 is the largest number that is the sum of the digits of its

cube.
28 is the 2

^{nd} perfect number.
29 is the 7

^{th} Lucas number.
30 is the largest number with the property that all smaller numbers

relatively prime to it are prime.
31 is a

Mersenne prime.
32 is the smallest non-trivial 5

^{th} power.

33 is the largest number that is not a sum of distinct

triangular numbers.
34 is the smallest number with the property that it and its neighbors have the same number of

divisors.
35 is the number of

hexominoes.
36 is the smallest non-trivial number which is both

square and triangular.
37 is the maximum number of 5

^{th} powers needed to sum to any number.

38 is the last

Roman numeral when written lexicographically.
39 is the smallest number which has 3 different

partitions into 3 parts with the same product.
40 is the only number whose letters are in alphabetical order.

41 is a value of n so that x

^{2} + x + n takes on

prime values for x = 0, 1, 2, ... n-2.
42 is the 5

^{th} Catalan number.
43 is the number of sided

7-iamonds.
44 is the number of

derangements of 5 items.
45 is a

Kaprekar number.
46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking

queens on a 9×9 chessboard.
47 is the largest number of

cubes that cannot tile a cube.
48 is the smallest number with 10

divisors.
49 is the smallest number with the property that it and its neighbors are

squareful.
50 is the smallest number that can be written as the sum of of 2

squares in 2 ways.
51 is the 6

^{th} Motzkin number.
52 is the 5

^{th} Bell number.
53 is the only two digit number that is reversed in

hexadecimal.
54 is the smallest number that can be written as the sum of 3

squares in 3 ways.
55 is the largest

triangular number in the Fibonacci sequence.
56 is the number of reduced 5×5

Latin squares.
57 = 111 in base 7.

58 is the number of

commutative semigroups of order 4.
59 is the number of

stellations of an icosahedron.
60 is the smallest number divisible by 1 through 6.

61 is the 3

^{rd} secant number.
62 is the smallest number that can be written as the sum of of 3 distinct

squares in 2 ways.
63 is the number of

partially ordered sets of 5 elements.
64 is the smallest number with 7

divisors.
65 is the smallest number that becomes

square if its reverse is either added to or subtracted from it.
66 is the number of

8-iamonds.
67 is the smallest number which is

palindromic in bases 5 and 6.
68 is the 2-digit string that appears latest in the decimal expansion of

π.
69 is a value of n where n

^{2} and n

^{3} together contain each digit once.

70 is the smallest

weird number.
71 divides the sum of the

primes less than it.
72 is the maximum number of

spheres that can touch another sphere in a lattice packing in 6 dimensions.
73 is the smallest multi-digit number which is one less than twice its reverse.

74 is the number of different non-

Hamiltonian polyhedra with a minimum number of vertices.
75 is the number of orderings of 4 objects with ties allowed.

76 is an

automorphic number.
77 is the largest number that cannot be written as a sum of distinct numbers whose

reciprocals sum to 1.
78 is the smallest number that can be written as the sum of of 4 distinct

squares in 3 ways.
79 is a permutable

prime.
80 is the smallest number n where n and n+1 are both products of 4 or more

primes.
81 is the

square of the sum of its digits.
82 is the number of

6-hexes.
83 is the number of

strongly connected digraphs with 4 vertices.
84 is the largest order of a

permutation of 14 elements.
85 is the largest n for which 1

^{2}+2

^{2}+3

^{2}+ ... +n

^{2} = 1+2+3+ ... +m has a solution.

86 = 222 in base 6.

87 is the sum of the

squares of the first 4 primes.
88 is one of only 2 numbers known whose

square has no isolated digits.
89 = 8

^{1} + 9

^{2}
90 is the number of degrees in a right angle.

91 is the smallest

pseudoprime in base 3.
92 is the number of different arrangements of 8 non-attacking

queens on an 8×8 chessboard.
93 = 333 in base 5.

94 is a

Smith number.
95 is the number of

planar partitions of 10.
96 is the smallest number that can be written as the difference of 2

squares in 4 ways.
97 is the smallest number with the property that its first 3 multiples contain the digit 9.

98 is the smallest number with the property that its first 5 multiples contain the digit 9.

99 is a

Kaprekar number.
100 is the smallest

square which is also the sum of 4 consecutive cubes.
101 is the number of

partitions of 13.
102 is the smallest number with three different digits.

103 has the property that placing the last digit first gives 1 more than triple it.

104 is the smallest known number of unit line segments that can exist in the plane, 4 touching at every vertex.

105 is the largest number n known with the property that n - 2

^{k} is

prime for k>1.
106 is the number of

trees with 10 vertices.
107 is the exponent of a

Mersenne prime.
108 is 3

hyperfactorial.
109 has a 5

^{th} root that starts 2.555555....

110 is the smallest number that is the product of two different substrings.

111 is the smallest possible magic constant of a 3×3

magic square of distinct primes.
112 is the side of the smallest

square that can be tiled with distinct integer-sided squares.
113 is a permutable

prime.
114 = 222 in base 7.

115 is the number of

rooted trees with 8 vertices.
116 is a value of n for which n! + 1 is

prime.
117 is the smallest possible value of the longest edge in a

Heronian Tetrahedron.
118 is the smallest number that has 4 different

partitions into 3 parts with the same product.
119 is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 8.

120 is the smallest number to appear 6 times in

Pascal's triangle.
121 is the only

square of the form 1 + n + n^{2} + n^{3} + n^{4}.
122 is the smallest number n>1 so that n concatenated with n-1 0's concatenated with the reverse of n is

prime.
123 is the 10

^{th} Lucas number.
124 is the smallest number with the property that its first 3 multiples contain the digit 2.

125 is the only number known that contains all its proper

divisors as proper substrings.
126 =

_{9}C_{4}.
127 is a

Mersenne prime.
128 is the largest number which is not the sum of distinct

squares.
129 is the smallest number that can be written as the sum of 3

squares in 4 ways.
130 is the number of functions from 6 unlabeled points to themselves.

131 is a permutable

prime.
132 is the smallest number which is the sum of all of the 2-digit numbers that can be formed with its digits.

133 is the smallest number n for which the sum of the

proper divisors of n divides φ(n).
134 =

_{8}C_{1} + _{8}C_{3} + _{8}C_{4}.
135 = 1

^{1} + 3

^{2} + 5

^{3}.

136 is the sum of the

cubes of the digits of the sum of the cubes of its digits.
137 is the smallest

prime with 3 distinct digits that remains prime if one of its digits is removed.
138 is a value of n for which n

!!! - 1 is prime.
139 is the number of unlabeled

topologies with 5 elements.
140 is a

harmonic divisor number.
141 is the 6

^{th} central trinomial coefficient.
142 is the number of

planar graphs with 6 vertices.
143 is the smallest quasi-Carmichael number in base 8.

144 is the largest

square in the Fibonacci sequence.
145 is a

factorion.
146 = 222 in base 8.

147 is the number of sided

6-hexes.
148 is the number of

perfect graphs with 6 vertices.
149 is the smallest number whose

square begins with three 2's.
150 = 10010110

_{2} = 2112

_{4} = 1100

_{5}, each using 2 different digits an equal number of times.

151 is a

palindromic prime.
152 has a

square composed of the digits 0-4.
153 is a

narcissistic number.
154 is the smallest number which is

palindromic in bases 6, 8, and 9.
155 is the sum of the

primes between its smallest and largest prime factor.
156 is the number of

graphs with 6 vertices.
157 is the smallest number with

φ(2n+1) < φ(2n).
158 is the number of

planar partitions of 11.
159 is the number of isomers of C

_{11}H

_{24}.

160 is the number of

9-iamonds.
161 is a

Cullen number.
162 is the smallest number that can be written as the sum of of 4 positive

squares in 9 ways.
163 is the largest

Heegner Number.
164 is the smallest number which is the concatenation of squares in two different ways.

165 is the midpoint of the n

^{th} larger prime and n

^{th} smaller prime, for 1 ≤ n ≤ 6.

166 is the number of monotone

Boolean functions of 4 variables.
167 is the smallest number whose 4

^{th} power begins with 4 identical digits

168 is the size of the smallest

non-cyclic simple group which is not an alternating group.
169 is the 7

^{th} Pell number.
170 is the smallest number n for which

φ(n) and σ(n) are both square.
171 has the same number of digits in

Roman numerals as its cube.
172 = 444 in base 6.

173 has a

square containing only 2 digits.
174 is the smallest number that can be written as the sum of of 4 positive distinct

squares in 6 ways.
175 = 1

^{1} + 7

^{2} + 5

^{3}.

176 is an

octagonal pentagonal number.
177 is the number of

graphs with 7 edges.
178 has a

cube with the same digits as another cube.
179 has a

square comprised of the digits 0-4.
180 is the total number of degrees in a triangle.

181 is a

strobogrammatic prime.
182 is the number of

connected bipartite graphs with 8 vertices.
183 is the smallest number n so that n concatenated with n+1 is

square.
184 is a

Kaprekar constant in base 3.
185 is the number of

conjugacy classes in the automorphism group of the 8 dimensional hypercube.
186 is the number of degree 11

irreducible polynomials over GF(2).
187 is the smallest quasi-Carmichael number in base 7.

188 is the number of

semigroups of order 4.
189 is a

Kaprekar constant in base 2.
190 is the largest number with the property that it and its ditinct

prime factors are palindromic in Roman numerals.
191 is a number n for which n, n+2, n+6, and n+8 are all

prime.
192 is the smallest number with 14

divisors.
193 is the largest number that can be written as ab + ac + bc with 0 < a < b < c in a unique way.

194 is the smallest number that can be written as the sum of 3

squares in 5 ways.
195 is the smallest value of n such that

_{2n}C_{n} is divisible by n^{2}.
196 is the smallest number that is not known to reach a

palindrome when repeatedly added to its reverse.
197 is a

Keith number.
198 = 11 + 99 + 88.

199 is the 11

^{th} Lucas number.
200 is the smallest number which can not be made

prime by changing one of its digits.
201 is a

Kaprekar constant in base 4.
202 has a

cube that contains only even digits.
203 is the 6

^{th} Bell number.
204 is the

square root of a triangular number.
205 = 5 × 41 = 541

_{6}.

206 is the smallest number whose English name contains all five vowels exactly once.

207 has a 4

^{th} power where the first half of the digits are a

permutation of the last half of the digits.
208 is the 10

^{th} Tetranacci number.
209 is the smallest quasi-Carmichael number in base 9.

210 is the product of the first 4

primes.
211 has a

cube containing only 3 different digits.
212 has a

square with 4/5 of the digits are the same.
213 is the number of

perfect squared rectangles of order 13.
214 is a value of n for which n

!! - 1 is prime.
215 = 555 in base 6.

216 is the smallest

cube that can be written as the sum of 3 cubes.
217 is a

Kaprekar constant in base 2.
218 is the number of

digraphs with 4 vertices.
219 is the number of

space groups, not including handedness.
220 is the smallest

amicable number.
221 is the number of

Hamiltonian planar graphs with 7 vertices.
222 is the number of

lattices on 8 unlabeled nodes.
223 is the smallest

prime p which has more primitive roots below p/2 than above p/2.
224 is the

Entringer number E(6,3).
225 is an

octagonal square number.
226 are the first 3 digits of

π^{226}.
227 is the number of

connected planar graphs with 8 edges.
228 is the number of ways, up to rotation and reflection, of dissecting a

regular 11-gon into 9 triangles.
229 is the smallest

prime that remains prime when added to its reverse.
230 is the number of

space groups, including handedness.
231 is the number of

partitions of 16.
232 is the number of 7×7

symmetric permutation matrices.
233 is the smallest number with the property that it and its neighbors can be written as a sum of 2

squares.
234 is the number of ways to stack 12 pennies in a line so that each penny lies on the table or on two pennies.

235 is the number of

trees with 11 vertices.
236 is the number of possible positions in Othello after 2 moves by both players.

237 is the smallest number with the property that its first 3 multiples contain the digit 7.

238 is the number of connected

partial orders on 6 unlabeled elements.
239 is the largest number that cannot be written as a sum of 8 or fewer

cubes.
240 is the smallest number with 20

divisors.
241 is the only number n for which the n

^{th} prime is π(n π(n)).
242 is the smallest n for which n, n+1, n+2, and n+3 have the same number of

divisors.
243 = 3

^{5}.

244 is the smallest number (besides 2) that can be written as the sum of 2

squares or the sum of two 5^{th} powers.
245 is a

stella octangula number.
246 =

_{9}C_{2} + _{9}C_{4} + _{9}C_{6}.
247 is the smallest possible difference between two

integers that together contain each digit exactly once.
248 is the smallest number n>1 for which the

arithmetic, geometric, and harmonic means of φ(n) and σ(n) are all integers.
249 is the index of a

prime Woodall number.
250 is the smallest multi-digit number so that the sum of the

squares of its prime factors equals the sum of the squares of its digits.
251 is the smallest number that can be written as the sum of 3

cubes in 2 ways.
252 is the 5

^{th} central binomial coefficient.
253 is the smallest non-trivial

triangular star number.
254 is the smallest multi-digit

composite number all of whose proper divisors contain the digit 2.
255 = 11111111 in base 2.

256 is the smallest non-trivial 8

^{th} power.

257 is a

Fermat prime.
258 is a value of n so that n(n+9) is a

palindrome.
259 = 1111 in base 6.

260 is the constant of an 8×8 magic square.

261 is the number of essentially different ways to dissect a

16-gon into 7 quadrilaterals.
262 is the 5

^{th} meandric number and the 9^{th} open meandric number.
263 is the largest known

prime whose square is strobogrammatic.
264 is the largest known number whose square is

undulating.
265 is the number of

derangements of 6 items.
266 is the

Stirling number of the second kind S(8,6).
267 is the number of

planar partitions of 12.
268 is the smallest number whose product of digits is 6 times the sum of its digits.

269 is the number of 6-octs.

270 is a

harmonic divisor number.
271 is the smallest

prime p so that p-1 and p+1 are divisible by cubes.
272 is the 4

^{th} tangent number.
273 = 333 in base 9.

274 is the

Stirling number of the first kind s(6,2).
275 is the number of

partitions of 28 in which no part occurs only once.
276 = 1

^{5} + 2

^{5} + 3

^{5}.

277 is a

Perrin number.
278 is the closest

integer to 6^{π}.
279 is the maximum number of 8

^{th} powers needed to sum to any number.

280 is the number of ways 18 people around a round table can shake hands in a non-crossing way, up to rotation.

281 is the sum of the first 14

primes.
282 is the number of planar partitions of 9.

283 = 2

^{5} + 8 + 3

^{5}.

284 is an

amicable number.
285 is the number of

binary rooted trees with 13 vertices.
286 is the number of

rooted trees with 9 vertices.
287 is the sum of consecutive

primes in 3 different ways.
288 is the smallest non-

palindrome non-square that when multiplied by its reverse is a square.
289 is a

Friedman number.
290 has a base 3 representation that ends with its base 6 representation.

291 is the largest number that is not the sum of distinct non-trivial powers.

292 is the number of ways to make change for a dollar.

293 is the number of ways to stack 20 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

294 is the number of

planar 2-connected graphs with 7 vertices.
295 is a structured deltoidal hexacontahedral number.

296 is the number of

partitions of 30 into distinct parts.
297 is a

Kaprekar number.
298 is a value of n so that n(n+3) is a

palindrome.
299 is the maximum number of regions a

cube can be cut into with 12 cuts.
300 is the largest possible score in bowling.

301 is a

6-hyperperfect number.
302 is the number of ways to play the first 3 moves in Checkers.

303 is the number of

bipartite graphs with 8 vertices.
304 is a

primitive semiperfect number.
305 is an hexagonal prism number.

306 is the number of 5-digit

triangular numbers.
307 is a non-

palindrome with a palindromic square.
308 is a

heptagonal pyramidal number.
309 is the smallest number whose 5

^{th} power contains every digit at least once.

310 = 1234 in base 6.

311 is a permutable

prime.
312 = 2222 in base 5.

313 is the number of intersections when all the diagonals of a

regular dodecagon are drawn.
314 is the smallest number that can be written as the sum of of 3 positive distinct

squares in 6 ways.
315 = (4+3) × (4+1) × (4+5).

316 has a digit product which is the digit sum of (3

^{1})

^{6}.

317 is the number of binary 4×4 matrices up to permutations of rows and columns.

318 is the number of unlabeled

partially ordered sets of 6 elements.
319 is the smallest number with the property that the

partition with the largest product does not have a maximum number of parts.
320 is the maximum

determinant of a binary 10×10 matrix.
321 is a

Delannoy number.
322 is the 12

^{th} Lucas number.
323 is the smallest

composite number n that divides the (n+1)^{st} Fibonacci number.
324 is the largest possible product of positive

integers with sum 16.
325 is a

3-hyperperfect number.
326 is the number of permutations of some subset of 5 elements.

327 is the largest number n so that n, 2n, and 3n together contain every digit from 1-9 exactly once.

328 concatenated with its successor is

square.
329 is the number of

forests with 10 vertices.
330 =

_{11}C_{4}.
331 is both a

centered pentagonal number and a centered hexagonal number.
332 is the number of

2-connected graphs with 7 vertices
333 is the number of

7-hexes.
334 is the number of

trees on 13 vertices with diameter 7.
335 is the number of degree 12

irreducible polynomials over GF(2).
336 =

_{8}P_{3}.
337 is the number of different resistances that can be created in a circuit of 8 equal resistors.

338 is the smallest number for which both the number of

divisors and the sum of its prime factors is a perfect number.
339 is the number of ways to divide 5 black and 5 white beads into piles.

340 is a value of n for which n! + 1 is

prime.
341 is the smallest

pseudoprime in base 2.
342 is the number of inequivalent binary

linear codes of length 8.
343 is a strong

Friedman number.
344 is the smallest number that can be written as the sum of a

cube and a 7^{th} power in more than one way.
345 is half again as large as the sum of its proper

divisors.
346 is a

Franel number.
347 is a

Friedman number.
348 is the smallest number whose 5

^{th} power contains exactly the same digits as another 5

^{th} power.

349 is a

Tetranacci-like number starting from 1, 1, 1, and 1.
350 is the

Stirling number of the second kind S(7,4).
351 is the smallest number so that it and the surrounding numbers are all products of 4 or more

primes.
352 is the number of different arrangements of 9 non-attacking

queens on an 9×9 chessboard.
353 is the smallest number whose 4

^{th} power can be written as the sum of four 4

^{th} powers.

354 is the sum of the first four 4

^{th} powers.

355 is the number of labeled

topologies with 4 elements.
356 is the smallest

happy number of height 6.
357 has a base 3 representation that ends with its base 7 representation.

358 has a base 3 representation that ends with its base 7 representation.

359 has a base 3 representation that ends with its base 7 representation.

360 is the number of degrees in a circle.

361 is the number of intersections on a Go board.

362 and its double and triple all use the same number of digits in

Roman numerals.
363 is a

perfect totient number.
364 =

_{14}C_{3}.
365 is the smallest number that can be written as a sum of consecutive

squares in more than 1 way.
366 is the number of days in a leap year.

367 is the largest number whose

square has strictly increasing digits.
368 is the number of ways to tile a 4×15 rectangle with the

pentominoes.
369 is the number of

octominoes.
370 is a

narcissistic number.
371 is a

narcissistic number.
372 is a

hexagonal pyramidal number.
373 is a permutable

prime.
374 is the smallest number that can be written as the sum of 3

squares in 8 ways.
375 is a

truncated tetrahedral number.
376 is an

automorphic number.
377 is the 14

^{th} Fibonacci number.
378 is the maximum number of regions a

cube can be cut into with 13 cuts.
379 is a value of n for which one more than the product of the first n

primes is prime.
380 is the number of necklaces possible with 13 beads, each being one of 2 colors.

381 is a

Kaprekar constant in base 2.
382 is the smallest number n with

σ(n) = σ(n+3).
383 is the number of

Hamiltonian graphs with 7 vertices.
384 = 8

!! = 12!!!!.
385 is the number of

partitions of 18.
386 is the number of regions the

complex plane is cut into by drawing lines between all pairs of 11^{th} roots of unity.
387 is the smallest number with

sort-then-add persistence of 10.
388 is the maximum value of n so
that there exist 6 denominations of stamps so that every postage from 1
to n can be paid for with at most 6 stamps.

389 is the smallest

prime so that it and the next 3 primes are all equal to 1 (mod 4).
390 is the number of

partitions of 32 into distinct parts.
391 ???

392 is a

Kaprekar constant in base 5.
393 is the 7

^{th} central trinomial coefficient.
394 is a

Schröder number.
395 does not occur in its

factorial in base 2.
396 is the number of 3×3 sliding puzzle positions that require exactly 11 moves to solve starting with the hole in a corner.

397 is a

Cuban prime.
398 is the number of

integers with complexity 22.
399 is a

Lucas-Carmichael number.
400 = 1111 in base 7.

401 is the number of

connected planar Eulerian graphs with 9 vertices.
402 is the number of

graphs with 8 vertices and 9 edges.
403 is the product of two

primes which are reverses of each other.
404 is the number of sided

10-hexes with holes.
405 is a

pentagonal pyramidal number.
406 is the number of ways to tile a 3×17 rectangle with 3×1 rectangles.

407 is a

narcissistic number.
408 is the 8

^{th} Pell number.
409 is the number of

graphs with 8 vertices with clique number 2.
410 is the smallest number that can be written as the sum of 2 distinct

prime powers in 2 ways.
411 is a member of the

Fibonacci-type sequence starting with 1 and 4.
412 is the number of subsets of {1,2,3,...,11} that have a sum divisible by 5.

413 is a structured hexagonal diamond number.

414 is a value of n for which n

^{4}, n

^{5}, n

^{6}, and n

^{7} have the same digit sum.

415 is the 10

^{th} Iccanobif number, where each term is the reverse of the sum of the previous two numbers.

416 is the number of subsets of the 15

^{th} roots of unity that add to a real number.
417 is the smallest number so that it and the next 3 numbers have different numbers of distinct

prime factors.
418 has the property that the sum of its

prime factors is equal to the product of its digits.
419 is the number of ways to divide a 6×6 grid of points into two sets using a straight line.

420 is the smallest number divisible by 1 through 7.

421 is the number of

commutative monoids of order 6.
422 is the smallest number whose 8

^{th} power has 21 digits.

423 is a number that does not have any digits in common with its

cube.
424 ???

425 is the number of subsets of {1,2,3,...,11} that have an

integer average.
426 is a

stella octangula number.
427 is a value of n for which n! + 1 is

prime.
428 has the property that its

square is the concatenation of two consecutive numbers.
429 is the 7

^{th} Catalan number.
430 is the number of necklaces possible with 6 beads, each being one of 4 colors.

431 is the index of a

prime Fibonacci number.
432 = 4 × 3

^{3} × 2

^{2}.

433 is the index of a

prime Fibonacci number.
434 is the smallest

composite value of n for which σ(n) + 2 = σ(n+2).
435 is the number of ordered

partitions of 16 into distinct parts.
436 is the smallest number whose

cube contains four 8's.
437 has a

cube with the last 3 digits the same as the 3 digits before that.
438 = 666 in base 8.

439 is the smallest

prime where inserting the same digit between every pair of digits never yields another prime.
440 is the number of

permutations of 12 items that fix 9 elements.
441 is the smallest

square which is the sum of 6 consecutive cubes.
442 is the number of

planar partitions of 13.
443 is a value of n for which

σ(n) is a repdigit.
444 is the largest known n for which there is a unique

integer solution to a_{1}+ ... +a_{n} = (a_{1})...(a_{n}).
445 has a base 10 representation which is the reverse of its base 9 representation.

446 is the smallest number that can be written as the sum of 3 distinct

squares in 8 ways.
447 is the smallest number of

convex quadrilaterals formed by 15 points in general position.
448 is the number of

10-iamonds.
449 has a base 3 representation that begins with its base 7 representation.

450 is the number of

13-iamonds with holes.
451 is the smallest number whose

reciprocal has period 10.
452 is the closest

integer to 7^{π}.
453 is the only number n so that n, 2n, and 6n together contain every digit exactly once.

454 is the largest number known that cannot be written as a sum of 7 or fewer

cubes.
455 =

_{15}C_{3}.
456 is the number of

tournaments with 7 vertices.
457 is the index of a

prime Euclid number.
458 is a number that does not have any digits in common with its

cube.
459 is the smallest number n for which reverse(n) - n contains the same digits as n.

460 ???

461 is the number of ways to stack 18 pennies in contiguous rows so that each penny lies on the table or on two pennies.

462 =

_{11}C_{5}.
463 is the smallest

prime so that it and the next 6 primes are all equal to 3 (mod 4).
464 is the maximum number of regions space can be divided into by 12

spheres.
465 is a

Kaprekar constant in base 2.
466 = 1234 in base 7.

467 has strictly increasing digits in bases 7, 9, and 10.

468 = 3333 in base 5.

469 is a value of n for which n! - 1 is

prime.
470 has a base 3 representation that ends with its base 6 representation.

471 is the smallest number with the property that its first 4 multiples contain the digit 4.

472 is the number of ways to tile a 5×5 square with

integer-sided squares.
473 is the largest known number whose

square and 4^{th} power use different digits.
474 is a member of the

Fibonacci-type sequence starting with 1 and 8.
475 has a

square that is composed of overlapping squares of smaller numbers.
476 is the number of different products of subsets of the set {1, 2, 3, ... 11}.

477 is the smallest number whose

cube contains four 3's.
478 is the 7

^{th} Pell-Lucas number.
479 is the number of sets of distinct positive

integers with mean 6.
480 is the smallest number which can be written as the difference of 2

squares in 8 ways.
481 is the number of

conjugacy classes in the automorphism group of the 10 dimensional hypercube.
482 is a number whose

square and cube use different digits.
483 is the last 3-digit string in the decimal expansion of

π.
484 is a

palindrome in base 3 and in base 10.
485 is the number of

categories with 6 morphisms and 2 objects.
486 is a

Perrin number.
487 is the number of

Hadamard matrices of order 28.
488 ???

489 is an

octahedral number.
490 is the number of

partitions of 19.
491 is the smallest number n so that the largest

prime factors of the numbers n through n+4 decrease.
492 is a

Hexanacci number.
493 is a

Lucas 7-step number.
494 is the number of unlabeled

distributive lattices with 14 elements.
495 is the

Kaprekar constant for 3-digit numbers.
496 is the 3

^{rd} perfect number.
497 is the number of

graphs with 8 edges.
498 is the number of necklaces possible with 8 beads, each being one of 3 colors.

499 is the number of ways to place 26 points on a 13×13 grid so that

no 3 points are on a line.
500 is the number of planar partitions of 10.

501 is the number of

partitions of 5 items into ordered lists.
502 uses the same digits as

φ(502).
503 is the smallest

prime which is the sum of the cubes of the first few primes.
504 =

_{9}P_{3}.
505 =

_{10}C_{5} + _{10}C_{0} + _{10}C_{5}.
506 is the sum of the first 11

squares.
507 is the number of

rooted ternary trees with 10 vertices.
508 ???

509 is the index of a

prime Fibonacci number.
510 is the number of

binary rooted trees with 14 vertices.
511 = 111111111 in base 2.

512 is the

cube of the sum of its digits.
513 is the number of

conjugacy classes of the alternating group A_{22}.
514 is the smallest number whose

cube begins with 13579.
515 is the number of

graphs on 6 vertices with no isolated vertices.
516 is the number of

partitions of 32 in which no part occurs only once.
517 does not occur in its

factorial in base 2.
518 = 5

^{1} + 1

^{2} + 8

^{3}.

519 is the number of

trees on 15 vertices with diameter 5.
520 is the number of ways to place 2 non-attacking kings on a 6×6 chessboard.

521 is the 13

^{th} Lucas number.
522 is the number of ways to place a non-attacking white and black pawn on a 6×6 chessboard.

523 is the smallest

prime that is followed by 17 composite numbers.
524 is the number of

6-kings.
525 is a

hexagonal pyramidal number.
526 is the number of ways to cut a 8×8 chessboard into 2 pieces with equal areas with a cut that only travels up and right.

527 is the smallest number n for which there do not exist 4 smaller numbers so that a

_{1}! a

_{2}! a

_{3}! a

_{4}! n! is

square.
528 concatenated with its successor is

square.
529 is the smallest number n so that the continued fraction for n/k contains no 2's for any 1 ≤ k ≤ n.

530 is the sum of the first 3

perfect numbers.
531 is the smallest number with the property that its first 4 multiples contain the digit 1.

532 is a hendecagonal pyramidal number.

533 is the number of

degree sequences for graphs with 5 vertices.
534 ???

535 is a

palindrome whose φ(n) is also palindromic.
536 is the number of solutions of the

stomachion puzzle.
537 divides the sum of the

cubes of the first 537 primes.
538 is the 10

^{th} open meandric number.
539 is the number of

multigraphs with 5 vertices and 9 edges.
540 is divisible by its reverse.

541 is the number of orderings of 5 objects with ties allowed.

542 is a member of the

Fibonacci-type sequence starting with 3 and 8.
543 is a number whose

square and cube use different digits.
544 is the

generalized Catalan number C(14,3).
545 has a base 3 representation that begins with its base 4 representation.

546

undulates in bases 3, 4, and 5.
547 is the smallest number that can not be written using 11 copies of 11 and the operations +, –, ×, and ÷.

548 is the maximum number of 9

^{th} powers needed to sum to any number.

549 ???

550 is a

pentagonal pyramidal number.
551 is the number of

trees with 12 vertices.
552 is the number of

prime knots with 11 crossings.
553 is a

Huay rhombic dodecahedral number.
554 is the number of self-dual

planar graphs with 20 edges.
555 is a

repdigit.
556 are the first 3 digits of 4

^{556}.

557 ???

558 divides the sum of the largest

prime factors of the first 558 positive integers.
559 is a

centered cube number.
560 =

_{16}C_{3}.
561 is the smallest

Carmichael number.
562 is the maximum number of regions a circle can be cut into by joining 11 points on the circumference with straight lines.

563 is the largest known

Wilson prime.
564 is the number of

13-ominoes with a horizontal or vertical line of symmetry.
565 is a structured truncated octahedral number.

566 is the number of ways to place 24 points on a 12×12 grid so that

no 3 points are on a line.
567 has the property that it and its

square together use the digits 1-9 once.
568 is the smallest number whose 7

^{th} power can be written as the sum of seven 7

^{th} powers.

569 is the smallest number n for which the concatenation of n, (n+1), ... (n+30) is

prime.
570 is the product of all the

prime palindromic Roman numerals.
571 is the index of a

prime Fibonacci number.
572 is the smallest number which has equal numbers of every digit in bases 2 and 3.

573 has the property that its

square is the concatenation of two consecutive numbers.
574 is the maximum number of pieces a

torus can be cut into with 14 cuts.
575 is a

palindrome that is one less than a square.
576 is the number of 4×4

Latin squares.
577 is a

Proth prime.
578 is the number of

graphs with 7 vertices with clique number 3.
579 is the number of

graphs with 7 vertices that have chromatic number 3.
580 is the 6

^{th} central quadrinomial coefficient.

581 has a base 3 representation that begins with its base 4 representation.

582 is the number of

antisymmetric relations on a 5 element set.
583 is the smallest number whose

reciprocal has period 26.
584 is the number of ways to color the vertices of a triangle with 12 colors, up to rotation.

585 is a

palindrome in base 2, base 8, and in base 10.
586 is the smallest number that appears in its

factorial 6 times.
587 is the smallest number whose digit sum is larger than that of its

cube.
588 is the number of possible rook moves on a 7×7 chessboard.

589 is a centered tetrahedral number.

590 is a value of n for which

φ(n) + φ(n+1) divides σ(n) + σ(n+1).
591 is the number of ways to stack 23 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

592 evenly divides the sum of its rotations.

593 is a

Leyland number.
594 = 1

^{5} + 2

^{9} + 3

^{4}.

595 is the number of ways to tile a 3×18 rectangle with 3×1 rectangles.

596 is the number of

Hamiltonian cycles of a 4×9 rectangle graph.
597 is a value of n for which n

!!! + 1 is prime.
598 = 5

^{1} + 9

^{2} + 8

^{3}.

599 is the smallest number whose digits add to 23.

600 and its reverse are both the averages of

twin primes.
601 is the location of the first occurrence of 3 consecutive zeroes in the decimal digits of

π.
602 are the first 3 digits of 5

^{602}.

603 is the smallest number n so that n, n+1, and n+2 are all the product of a

prime and the square of a prime.
604 and the two numbers before it and after it are all products of exactly 3

primes.
605 has a sum of digits equal to its largest

prime factor.
606 is the first non-trivial number that is both 11-gonal and centered 11-gonal.

607 is the exponent of a

Mersenne prime.
608 is a number that does not have any digits in common with its

cube.
609 is a

strobogrammatic number.
610 is the smallest

Fibonacci number that begins with 6.
611 ???

612 is a number whose

square and cube use different digits.
613 is the index of a

prime Lucas number.
614 is the smallest number that can be written as the sum of 3

squares in 9 ways.
615 is the

trinomial coefficient T(10,6).
616 is a

Padovan number.
617 = 1!

^{2} + 2!

^{2} + 3!

^{2} + 4!

^{2}.

618 is the number of

ternary square-free words of length 15.
619 is a

strobogrammatic prime.
620 is the number of sided

7-hexes.
621 is the number of ways to 9-color the faces of a

tetrahedron.
622 ???

623 is the number of inequivalent asymmetric

Ferrers graphs with 23 points.
624 is the smallest number with the property that its first 5 multiples contain the digit 2.

625 is an

automorphic number.
626 is a

palindrome in base 5 and in base 10.
627 is the number of

partitions of 20.
628 is the sum of the

squares of 4 consecutive primes.
629 evenly divides the sum of its rotations.

630 is a

triangular number, 3 times a triangular number, and 6 times a triangular number.
631 has a base 2 representation that begins with its base 5 representation.

632 is the number of triangles formed by connecting the diagonals of a regular octagon.

633 is the smallest number n whose 5

^{th} root has a decimal part that begins with the digits of n.

634 is a number n whose 5

^{th} root has a decimal part that begins with the digits of n.

635 is a number n whose 5

^{th} root has a decimal part that begins with the digits of n.

636 is a number n whose 5

^{th} root has a decimal part that begins with the digits of n.

637 = 777 in base 9.

638 is the number of fixed

5-kings.
639 is a number n whose 5

^{th} root has a decimal part that begins with the digits of n.

640 = 16

!!!!!!.
641 is the smallest

prime factor of 2^{25}+1.
642 is the smallest number with the property that its first 6 multiples contain the digit 2.

643 is the largest

prime factor of 123456.
644 is a

Perrin number.
645 is the largest n for which 1+2+3+ ... +n = 1

^{2}+2

^{2}+3

^{2}+ ... +k

^{2} for some k.

646 is the number of

connected planar graphs with 7 vertices.
647 ???

648 is the smallest number whose decimal part of its 6

^{th} root begins with the digits 1-9 in some order.

649 is the smallest number n so that n

^{2} is 1 more than 13 times a

square.
650 is the sum of the first 12

squares.
651 has a 4

^{th} power that is the sum of four 4

^{th} powers.

652 is the only known

non-perfect number whose number of divisors and sum of smaller divisors are perfect.
653 is the only known

prime for which 5 is neither a primitive root or a quadratic residue of 4n^{2}+1.
654 has a

square that is the sum of a cube and 5^{th} power.
655 ???

656 is a

palindrome in base 3 and in base 10.
657 is the number of ways to tile a 4×22 rectangle with 4×1 rectangles.

658 is the number of triangles of any size contained in the triangle of side 13 on a triangular grid.

659 is an Eisenstein-Mersenne prime.

660 is the order of a

non-cyclic simple group.
661 is the largest

prime factor of 8! + 1.
662 is the index of the smallest

triangular number that contains the digits 1, 2, 3, 4, and 5.
663 is the

generalized Catalan number C(15,3).
664 is a value of n so that n(n+7) is a

palindrome.
665 is a member of the

Fibonacci-type sequence starting with 1 and 4.
666 is the largest rep-digit

triangular number.
667 is the number of asymmetric

trees with 16 vertices.
668 is the number of legal pawn moves in Chess.

669 is the number of unsymmetrical ways to dissect a

regular 12-gon into 10 triangles.
670 is an

octahedral number.
671 is a

rhombic dodecahedral number.
672 is a

multi-perfect number.
673 is a

Tetranacci-like number starting from 1, 1, 1, and 1.
674 ???

675 is the smallest order for which there are 17

groups.
676 is the smallest

palindromic square number whose square root is not palindromic.
677 is the closest

integer to 11^{e}.
678 is a member of the

Fibonacci-type sequence starting with 1 and 7.
679 is the smallest number with

multiplicative persistence 5.
680 is the smallest

tetrahedral number that is also the sum of 2 tetrahedral numbers.
681 divides the sum of the first 681

composite numbers.
682 =

_{11}C_{6} + _{11}C_{8} + _{11}C_{2}.
683 is a

Wagstaff prime.
684 is the sum of 3 consecutive

cubes.
685 ???

686 is the number of

partitions of 35 in which no part occurs only once.
687 is the closest

integer to 8^{π}.
688 is a

Friedman number.
689 is the smallest number that can be written as the sum of 3 distinct

squares in 9 ways.
690 is the smallest number that can not be written as the sum of a

triangular number, a cube, and a Fibonacci number.
691 is the smallest

prime p for which x^{5} = x^{4} + x^{3} + x^{2} + x + 1 (mod p) has 5 solutions.
692 is a number that does not have any digits in common with its

cube.
693 are the first 3 decimal digits of

ln(2).
694 is the number of different arrangements (up to rotation and reflection) of 7 non-attacking

rooks on a 7×7 chessboard.
695 is the maximum number of pieces a

torus can be cut into with 15 cuts.
696 is a

palindrome n so that n(n+8) is also palindromic.
697 is a

12-hyperperfect number.
698 = 3

^{2} + 4

^{3} + 5

^{4}.

699 is a value of n for which |cos(n)| is smaller than any previous

integer.
700 is the number of symmetric 8-cubes.

701 = 1

^{0} + 2

^{1} + 3

^{2} + 4

^{3} + 5

^{4}.

702 ???

703 is a

Kaprekar number.
704 is the number of sided

octominoes.
705 is the smallest

Lucas pseudoprime.
706 ???

707 is the smallest number whose

reciprocal has period 12.
708 is the maximum value of n so
that there exist 4 denominations of stamps so that every postage from 1
to n can be paid for with at most 12 stamps.

709 is the number of

connected planar graphs with 9 edges.
710 is the number of

connected graphs with 9 edges.
711 is the name of a chain of convenience stores.

712 is the largest number known that does not have any digits in common with its 8

^{th} power.

713 is the number of

commutative monoids of order 7 with 4 idempotents.
714 is the smallest number which has equal numbers of every digit in bases 2 and 5.

715 =

_{13}C_{4}.
716 is the smallest number whose

cube contains four 6's.
717 is a

palindrome in base 2 and in base 10.
718 is the number of unlabeled

topologies with 6 elements.
719 is the number of

rooted trees with 10 vertices.
720 = 6!

721 is the smallest number which can be written as the difference of 2

cubes in 2 ways.
722 is the sum of the 4

^{th} powers of the first 3

primes.
723 = (1!)! + (2!)! + (3!)!.

724 is the number of different arrangements of 10 non-attacking

queens on an 10×10 chessboard.
725 ???

726 is the number of 4-step self-avoiding walks on the cubic lattice.

727 has the property that its

square is the concatenation of two consecutive numbers.
728 is the smallest number n where n and n+1 are both products of 5 or more

primes.
729 = 3

^{6}.

730 is the number of

connected bipartite graphs with 9 vertices.
731 is the number of

planar partitions of 14.
732 = 1

^{7} + 2

^{6} + 3

^{5} + 4

^{4} + 5

^{3} + 6

^{2} + 7

^{1}.

733 is the sum of the digits of 4

^{44}.

734 is the smallest number that can be written as the sum of 3 distinct non-zero

squares in 10 ways.
735 is the smallest number that is the concatenation of its distinct

prime factors.
736 is a strong

Friedman number.
737 is a Boeing plane.

738 = 6 + 66 + 666.

739 has a base 2 representation that begins with its base 9 representation.

740 is the number of

self-avoiding walks of length 8.
741 is the number of

multigraphs with 6 vertices and 8 edges.
742 is the smallest number that is one more than triple its reverse.

743 is the number of

independent sets of the graph of the 4-dimensional hypercube.
744 is the number of

perfect squared rectangles of order 14.
745 is the smallest number whose

square begins with three 5's.
746 = 1

^{7} + 2

^{4} + 3

^{6}.

747 is a Boeing plane.

748 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner.

749 is the number of ways to divide a 7×7 grid of points into two sets using a straight line.

750 is the

Stirling number of the second kind S(10,8).
751 is the index of a

prime Woodall number.
752 is the number of

conjugacy classes in the automorphism group of the 11 dimensional hypercube.
753 is the smallest number whose

cube contains 4 consecutive 7's.
754 ???

755 is the number of

trees on 14 vertices with diameter 6.
756 is the maximum number of regions space can be divided into by 14

spheres.
757 is the smallest number whose

reciprocal has a period of 27.
758 ???

759 is the number of octads in the

large Witt design.
760 is the number of

partitions of 37 into distinct parts.
761 ???

762 is the starting location of 999999 in the decimal expansion of

π.
763 is the smallest number whose 4

^{th} power contains every digit at least once.

764 is the number of 8×8

symmetric permutation matrices.
765 is a

Kaprekar constant in base 2.
766 is the number of

series-reduced planted trees with 9 leaves.
767 is the largest n so that n

^{2} =

_{m}C_{0} + _{m}C_{1} + _{m}C_{2} + _{m}C_{3} has a solution.
768 is the number of subsets of {1,2,3,...,12} that have an

integer average.
769 is the total number of digits of all

binary numbers of length 1-7.
770 is the number of digits of the 15

^{th} perfect number.
771 is the number of intersections when all the diagonals of a

regular 14-gon are drawn.
772 ???

773 is the smallest odd number n so that n+2

^{k} is

composite for all k<n.
774 ???

775 is the smallest number whose 9

^{th} power has 26 digits.

776 ???

777 is a

repdigit in base 6 and in base 10.
778 is the number of ways a 5×1 rectangle can be surrounded by 5×1 rectangles.

779 ???

780 = (5+7) × (5+8) × (5+0).

781 = 11111 in base 5.

782 is a number whose sum of

divisors is a 4^{th} power.
783 is the number of

11-ominoes that tile the plane by translation.
784 is the sum of the first 7

cubes.
785 are the last 3 digits of the sum of the first 785

squares.
786 is the largest known n for which

_{2n}C_{n} is not divisible by the square of an odd prime.
787 is a

palindrome in base 3 and in base 10.
788 is the smallest of 6 consecutive numbers divisible by 6 consecutive

primes.
789 are the first 3 digits of 9

^{789}.

790 ???

791 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 12.

792 is the number of

partitions of 21.
793 is one less than twice its reverse.

794 = 1

^{6} + 2

^{6} + 3

^{6}.

795 is a number whose sum of

divisors is a 4^{th} power.
796 ???

797 is the number of

functional graphs on 9 vertices.
798 is the number of

ternary square-free words of length 16.
799 is the smallest number whose sum of digits is

composite and whose sum of digits cubed is prime.
800 = 2222 in base 7.

801 = (7! + 8! + 9! + 10!) / (7 × 8 × 9 × 10).

802 is the number of isomers of C

_{13}H

_{28}.

803 is a value of n for which

σ(n) is a repdigit.
804 is a value of n for which 2

φ(n) = φ(n+1).
805 is the number of possible positions in Checkers after 4 moves.

806 is not the sum of a

square, a cube, a 4^{th} power, and a 5^{th} power.
807 ???

808 is a

strobogrammatic number.
809 is a member of the

Fibonacci-type sequence starting with 1 and 5.
810 is a value of n for which n-1 and n+1 are

twin primes, and so are 2n-1 and 2n+1.
811 is the smallest

prime factor of 24! + 1.
812 is the number of triangles of any size contained in the triangle of side 14 on a triangular grid.

813 are the first 3 digits of 813

^{e}.

814 is a value of n so that n(n+5) is a

palindrome.
815 is a

Lucas 3-step number.
816 =

_{18}C_{3}.
817 ???

818 is the number of ways to dissect a 12-gon using non-crossing diagonals into polygons with an even number of sides.

819 is the smallest number so that it and its successor are both the product of 2

primes and the square of a prime.
820 = 1111 in base 9.

821 is a number n for which n, n+2, n+6, and n+8 are all

prime.
822 is the number of

planar graphs with 7 vertices.
823 is a number that does not have any digits in common with its

cube.
824 ???

825 is the number of ways to legally add 2 sets of parentheses to a product of 9 variables.

826 ???

827 is the number of asymmetric

trees with 11 vertices.
828 ???

829 is a value of n for which

π(n) is the product of the digits of n.
830 ???

831 is the number of

monic polynomials of degree 9 with integer coefficients whose complex roots are all in the unit disk.
832 is the maximum number of pieces a

torus can be cut into with 16 cuts.
833 is a centered octahedral number.

834 is the maximum number of regions a

cube can be cut into with 17 cuts.
835 is the 9

^{th} Motzkin number.
836 is a non-

palindrome with a palindromic square.
837 ???

838 ???

839 has a base 5 representation that begins with its base 9 representation.

840 is the smallest number divisble by 1 through 8.

841 is a

square that is also the sum of 2 consecutive squares.
842 is the ratio of

Fibonacci numbers.
843 is the 14

^{th} Lucas number.
844 is the smallest number so that it and the next four numbers are

squareful numbers.
845 ???

846 has the property that its

square is the concatenation of two consecutive numbers.
847 is the sum of the digits of the 14

^{th} Mersenne prime.
848 is the number of inequivalent binary

linear codes of length 9.
849 is a value of n for which

σ(n-1) = σ(n+1).
850 is the number of

trees on 14 vertices with diameter 7.
851 is the number of ordered

partitions of 18 into distinct parts.
852 is the number of

6-colorable connected graphs with 7 vertices.
853 is the number of

connected graphs with 7 vertices.
854 has the property that it and its

square together use the digits 1-9 once.
855 is the smallest number which is the sum of 5 consecutive

squares or 2 consecutive cubes.
856 is a member of the

Fibonacci-type sequence starting with 1 and 9.
857 is a value of n for which

φ(n) = φ(n-1) + φ(n-2).
858 is the smallest

palindrome with 4 different prime factors.
859 is the number of planar partitions of 11.

860 ???

861 = 7 + 77 + 777.

862 is a number whose sum of

divisors is a 4^{th} power.
863 is a value of n so that n(n+6) is a

palindrome.
864 is the number of

partitions of 38 into distinct parts.
865 ???

866 is the number of sided

10-iamonds.
867 is the number of

graphs with 8 vertices that have chromatic number 5.
868 has a

square root whose decimal part starts with the digits 1-9 in some order.
869 is the number of different resistances that can be created in a circuit of 9 equal resistors.

870 is the sum of its digits and the

cube of its digits.
871 ???

872 is a value of n for which n! + 1 is

prime.
873 = 1! + 2! + 3! + 4! + 5! + 6!

874 is the number of positive integer solutions to (1 + 1/a)(1 + 1/b)(1 + 1/c)(1 + 1/d)(1 + 1/e) = 2.

875 is

3-automorphic.
876 is a dodecagonal pyramidal number.

877 is the 7

^{th} Bell number.
878 is the number of 3×3 sliding puzzle positions that require exactly 29 moves to solve starting with the hole on a side.

879 is a number n whose 5

^{th} root has a decimal part that begins with the digits of n.

880 is the number of 4×4

magic squares.
881 is a number n whose 5

^{th} root has a decimal part that begins with the digits of n.

882 is the smallest number whose

square begins with three 7's.
883 is a number n whose 5

^{th} root has a decimal part that begins with the digits of n.

884 is a number n whose 5

^{th} root has a decimal part that begins with the digits of n.

885 is an enneagonal pyramidal number.

886 ???

887 is a value of n for which

σ(n) is a repdigit.
888 and the following 18 numbers are

composite.
889 is a

Kaprekar constant in base 2.
890 ???

891 is the number of unlabeled

distributive lattices with 15 elements.
892 is the smallest integer ratio of a 13-digit number to its product of digits.

893 has a

square whose digits each occur twice.
894 has a base 5 representation that begins with its base 9 representation.

895 is a

Woodall number.
896 is not the sum of 4 non-zero

squares.
897 is a

Cullen number.
898 is a member of the

Fibonacci-type sequence starting with 2 and 5.
899 is the product of

twin primes.
900 has a base 5 representation that begins with its base 9 representation.

901 is the sum of the digits of the first 100 positive

integers.
902 is a value of n so that n(n+7) is a

palindrome.
903 is the 6

^{th} super Catalan number
904 has a

cube that is the sum of 3 positive cubes.
905 is the smallest

composite number that is not the sum of a prime and a power of 2.
906 is the number of

perfect graphs with 7 vertices.
907 is the largest n so that

**Q**(√n) has class number 3.
908 ???

909 is a value of n that has has no digits in common with 2n, 3n, 4n, 5n, 6n, 7n, 8n, or 9n.

910 is the

generalized Catalan number C(11,4).
911 is the American emergency number.

912 is a

Pentanacci number.
913 has exactly the same digits in 3 different bases.

914 is the number of

binary rooted trees with 15 vertices.
915 ???

916 is a

strobogrammatic number.
917 is the only positive number known whose 9

^{th} power can be written as the sum of ten 9

^{th} powers.

918 is a number that does not have any digits in common with its

cube.
919 is the smallest number which is not the difference between

palindromes.
920 is a truncated cube number.

921 ???

922 = 1234 in base 9.

923 multiplied by its successor gives a number concatenated with itself.

924 is the 6

^{th} central binomial coefficient.
925 is the number of

partitions of 37 in which no part occurs only once.
926 is the smallest number that can not be formed using the digits 1-6 at most once, with the operators +, –, ×, ÷, and ^.

927 is the 13

^{th} tribonacci number.
928 ???

929 is a

Proth prime.
930 is the number of

even permutations on 7 elements with no fixed points.
931 ???

932 ???

933 is a house number.

934 has a 5

^{th} root that starts 3.25252225....

935 is a

Lucas-Carmichael number.
936 is a

pentagonal pyramidal number.
937 ???

938 is the number of lines passing through at least 2 points of an 8×8 grid of points.

939 has a

cube root whose decimal part starts with the digits 1-9 in some order.
940 is the maximum number of regions space can be divided into by 15

spheres.
941 is the smallest number which is the reverse of the sum of its proper substrings.

942 is the smallest number whose

cube contains five 8's.
943 is a

Lucas 6-step number.
944 ???

945 is the smallest odd

abundant number.
946 is a

hexagonal pyramidal number.
947 ???

948 is the number of symmetric

plane partitions of 24.
949 is the larger number in a

Ruth-Aaron pair.
950 is the

generalized Catalan number C(17,3).
951 is the number of functions from 8 unlabeled points to themselves.

952 = 9

^{3} + 5

^{3} + 2

^{3} + 9 × 5 × 2.

953 is the largest

prime factor of 54321.
954 ???

955 is the number of ways to to arrange the numbers 1-9 around a circle so that the sums of adjacent numbers are distinct.

956 is the number of

multigraphs with 16 vertices and 4 edges.
957 is a value of n for which

σ(n) = σ(n+1).
958 is the number of labeled

3-colorable graphs with 5 vertices.
959 is a

Carol number.
960 is the sum of its digits and the

cube of its digits.
961 is a

square whose digits can be rotated to give another square.
962 ???

963 is a value of n for which

π(n) is the product of the digits of n.
964 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in the center.

965 ???

966 is the

Stirling number of the second kind S(8,3).
967 is the number of 6-digit

triangular numbers.
968 is an

Achilles number.
969 is a tetrahedral

palindrome.
970 is the number of

connected graphs with 8 vertices and 17 edges.
971 ???

972 is an

Achilles number.
973 is the number of inequivalent asymmetric

Ferrers graphs with 25 points.
974 is the number of

multigraphs with 5 vertices and 10 edges.
975 is the number of

11-ominoes that contain 1 hole.
976 has a

square formed by inserting a block of digits inside itself.
977 is a

Stern prime.
978 2

^{4} + 3

^{4} + 4

^{4} + 5

^{4}.

979 is the sum of the first five 4

^{th} powers.

980 is the number of

trees on 23 vertices with diameter 4.
981 is the smallest number that has 5 different

partitions into 3 parts with the same product.
982 is the number of

partitions of 39 into distinct parts.
983 is a

Wedderburn-Etherington number.
984 = 8 + 88 + 888.

985 is the 9

^{th} Pell number.
986 is a

strobogrammatic number.
987 is the 16

^{th} Fibonacci number.
988 is the maximum number of regions a

cube can be cut into with 18 cuts.
989 is the smallest number so that it and its reverse are divisible by 43.

990 is a

triangular number that is the product of 3 consecutive integers.
991 is a permutable

prime.
992 is the number of differential structures on the 11-dimensional

hypersphere.
993 is the number of paraffins with 8 carbon atoms.

994 is the smallest number with the property that its first 18 multiples contain the digit 9.

995 has a

square formed by inserting a block of digits inside itself.
996 has a

square formed by inserting a block of digits inside itself.
997 has a

cube root that starts 9.98998998....
998 is the smallest number with the property that its first 55 multiples contain the digit 9.

999 is a

Kaprekar number.
1000 = 10

^{3}.

1001 is the smallest

palindromic product of 3 consecutive primes.
1002 is the number of

partitions of 22.
1003 has a base 2 representation that ends with its base 3 representation.

1004 is a

Heptanacci number.
1005 is a decagonal pyramidal number.

1006 has a

cube that is a concatenation of other cubes.
1007 is the maximum value of n so
that there exist 8 denominations of stamps so that every postage from 1
to n can be paid for with at most 6 stamps.

1008 is the number of symmetric ways to fold a strip of 16 stamps.

1009 is the

pseudosquare modulo 7.
1010 is the number of ways to tile a 5×12 rectangle with the

pentominoes.
1011 has a

square that is formed by inserting three 2's into it.
1012 has a

square that is formed by inserting three 4's into it.
1013 is the number of ways 10 people can line up so that only one person has a taller person in front of him.

1014 is the smallest number that can be written in 7 ways as the sum of a number and the product of its non-zero digits.

1015 is the number of

chiral invertible knots with 12 crossings.
1016 is a

stella octangula number.
1017 is the smallest number whose

square contains 7 different digits.
1018 is the number of

isohedral 8-hexes.
1019 is a value of n for which one more than the product of the first n

primes is prime.
1020 is the number of ways to place 2 non-attacking kings on a 7×7 chessboard.

1021 is a value of n for which one more than the product of the first n

primes is prime.
1022 is a

Friedman number.
1023 is the smallest number with 4 different digits.

1024 is the smallest number with 11

divisors.
1025 is the smallest number that can be written as the sum of a

square and a cube in 4 ways.
1026 is the number of subsets of the 22

^{nd} roots of unity that add to 1.
1027 is the sum of the

squares of the first 8 primes.
1028 only requires the digits 0-9 to be written in bases 2-18.

1029 is the smallest order for which there are 19

groups.
1031 is the length of the largest

repunit that is known to be prime.
1032 is the smallest number that can be written as the sum of a

cube and a 5^{th} power in more than one way.
1033 = 8

^{1} + 8

^{0} + 8

^{3} + 8

^{3}.

1035 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
1036 = 4444 in base 6.

1037 is a value of n for which

φ(n) = φ(n-1) + φ(n-2).
1038 is the number of ways to stack 29 pennies in contiguous rows so that each penny lies on the table or on two pennies.

1039 is the number of different resistances that can be formed by nine or fewer 1-ohm resistors in series or parallel.

1040 is the number of the standard IRS tax form.

1041 does not occur in its

factorial in base 2.
1042 has the property that if each digit is replaced by its

cube, the resulting number is a cube.
1043 has a 5

^{th} power that contains only digits 4 and smaller.

1044 is the number of

graphs with 7 vertices.
1045 is an octagonal pyramidal number.

1046 is the smallest number whose

cube contains 4 consecutive 4's.
1049 is an Eisenstein-Mersenne prime.

1050 is the

Stirling number of the second kind S(8,5).
1051 is the smallest value of n for which

π(8n) = n.
1052 has the property that placing the last digit first gives 1 more than twice it.

1053 divides the sum of the digits of 2

^{1053} × 1053!.

1054 is a value of n for which |cos(n)| is smaller than any previous

integer.
1055 is the maximum value of n so
that there exist 5 denominations of stamps so that every postage from 1
to n can be paid for with at most 10 stamps.

1056 is the area of the smallest non-

square rectangle that can be tiled with integer-sided squares.
1057 is the number of

idempotent functions from a set of 6 elements into itself.
1060 is the sum of the

primes less than 100.
1061 is the smallest

emirp which is a different emirp when viewed upside down.
1063 is not the sum of a

square, a cube, a 4^{th} power, and a 5^{th} power.
1066 is a value of n for which 2

φ(n) = φ(n+1).
1067 has exactly the same digits in 3 different bases.

1069 is a

prime that remains prime when preceded and followed by one, two, three, or four 3's.
1071 is the sum of 3 consecutive

cubes.
1072 is the smallest number that can be written as the sum of 2, 3, 4, or 5 positive

cubes.
1075 is the number of squares of functions from a set of 5 elements to itself.

1076 is a member of the

Fibonacci-type sequence starting with 1 and 4.
1077 is a value of n for which n

!!! + 1 is prime.
1078 is the number of

lattices on 9 unlabeled nodes.
1079 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 15.

1080 is the smallest number with 18

divisors.
1081 is a

triangular number that is the product of two primes.
1084 is the smallest number whose English name contains all five vowels in order.

1086 is the number of

13-hexes with reflectional symmetry.
1087 is a

Kynea prime.
1088 has a sum of digits equal to its largest

prime factor.
1089 is one ninth of its reverse.

1092 is the order of a

non-cyclic simple group.
1093 is the smallest

Wieferich prime.
1094 is the maximum value of n so
that there exist 4 denominations of stamps so that every postage from 1
to n can be paid for with at most 14 stamps.

1095 is the number of vertices in a

Sierpinski triangle of order 6.
1096 is the number of subsets of {1,2,3,...,14} that have a sum divisible by 15.

1097 is the closest

integer to e^{7}.
1098 = 11 + 0 + 999 + 88.

1099 = 1 + 0 + 999 + 99.

1100 has a base 3 representation that ends with 1100.

1101 has a base 2 representation that ends with 1101.

1102 is the number of

connected graphs with 10 vertices and 36 edges.
1103 is the number of

graphs with 9 vertices and 8 edges.
1104 is a

Keith number.
1105 is the smallest number that can be written as the sum of 2

squares in 4 ways.
1107 is the 8

^{th} central trinomial coefficient.
1109 is the only 4 digit number whose 2-digit substrings are consecutive.

1110 is the sum of all numbers with digit sum 3 with 3 or fewer digits.

1111 is a

repdigit.
1112 has a base 3 representation that begins with 1112.

1113 is the number of

partitions of 40 into distinct parts.
1114 = 1

^{2} + 2

^{3} + 3

^{4} + 4

^{5}.

1115 is a number n for which

φ(n) is a repdigit.
1116 is the number of

8-abolos.
1117, when followed by any of its digits, is

prime.
1118 is the number of

graphs with 9 vertices that have chromatic number 2.
1119 is the number of

bipartite graphs with 9 vertices.
1120 = (1 × 2 × 3 × 4 × 5 × 6 × 7 × 8) / (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8).

1121 is the smallest number that can not be written using 12 copies of 12 and the operations +, –, ×, and ÷.

1122 =

_{33}C_{1} + _{33}C_{1} + _{33}C_{2} + _{33}C_{2}.
1123 has digits which start the

Fibonacci sequence.
1124 is a

Leyland number.
1125 is a hendecagonal pyramidal number.

1127 has the property that if each digit is replaced by its

square, the resulting number is a square.
1128 is an icosahedral number.

1130 is a

Perrin number.
1131 has the property that the concatenation of its

prime factors in increasing order is a square.
1132 is the number of

3-valent trees with 15 vertices.
1134 is the number of

permutations of 9 items that fix 5 elements.
1135 is the number of ways to color the vertices of a triangle with 15 colors, up to rotation.

1137 is the maximum value of n so
that there exist 7 denominations of stamps so that every postage from 1
to n can be paid for with at most 7 stamps.

1139 has the property that placing the last digit first gives 1 more than 8 times it.

1140 is the only number less than
10 million that can be written in 2 different ways as the sum of 3 or
more consecutive numbers raised to consecutive powers.

1141 is the smallest number whose 6

^{th} power can be written as the sum of seven 6

^{th} powers.

1142 is the number of ways to place a non-attacking white and black pawn on a 7×7 chessboard.

1144 is the number of

non-invertible knots with 12 crossings.
1146 divides the sum of the digits of 2

^{1146} × 1146!.

1147 is the product of two consecutive

primes.
1148 is the number of ways to fold a strip of 9 stamps.

1150 is the number of

11-iamonds without bilateral symmetry.
1151 is the smallest number that can be written as the sum of consecutive

primes in exactly 4 ways.
1152 is a

highly totient number.
1153 is the smallest number with the property that its first 3 multiples contain the digit 3.

1154 is the 8

^{th} Pell-Lucas number.
1155 is the

Stirling number of the second kind S(11,9).
1156 is a

square whose digits are non-decreasing.
1157 is the number of

anisohedral 15-ominoes.
1158 is the maximum number of pieces a

torus can be cut into with 18 cuts.
1159 is a centered octahedral number.

1160 is the maximum number of regions a

cube can be cut into with 19 cuts.
1161 is the number of

11-iamonds without holes.
1165 is the number of

conjugacy classes in the automorphism group of the 12 dimensional hypercube.
1166 is a

heptagonal pyramidal number.
1167 is the smallest number whose 8

^{th} power can be written as the sum of nine 8

^{th} powers.

1168 is the number of binary

cube-free words of length 16.
1169 is the number of

connected graphs with 8 vertices and 12 edges.
1170 = 2222 in base 8.

1171 has a 4

^{th} power containing only 4 different digits.

1172 is the number of subsets of {1,2,3,...,14} that have a sum divisible by 14.

1177 is a number whose sum of

divisors is a 4^{th} power.
1179 is the number of different

permanents of binary 7×7 matrices.
1182 is the number of necklaces (that can't be turned over) possible with 14 beads, each being one of 2 colors.

1183 is the smallest number with the property that its first 4 multiples contain the digit 3.

1184 is an

amicable number.
1185 = 11 + 1111 + 8 + 55.

1186 is the number of

11-iamonds.
1187 = 111 + 111 + 888 + 77.

1188 is the number of triangles of any size contained in the triangle of side 16 on a triangular grid.

1189 is the

square root of a triangular number.
1191 is the number of symmetric

plane partitions of 25.
1192 is the number of

12-iamonds that do not tile the plane.
1193 and its reverse are

prime, even if we append or prepend a 3 or 9.
1196 is the number of lines through exactly 2 points of a 9×9 grid of points.

1197 is the smallest number that contains as substrings the maximal

prime powers that divide it.
1200 = 3333 in base 7.

1201 has a

square that is formed by inserting three 4's into it.
1202 has the property that the concatenation of its

prime factors in increasing order is a square.
1203 is the smallest number n for which the concatenation of n, (n+1), ... (n+34) is

prime.
1204 is the magic constant for a 7×7×7

magic cube.
1205 is the number of

fullerenes with 58 carbon atoms.
1206 is a

Friedman number.
1207 is the product of two

primes which are reverses of each other.
1209 = 1 × 3 × 13 × 31.

1210 is an

amicable number.
1211 is the smallest number that ends an arithmetic progression of 9 numbers with the same

prime signature.
1212 is the number of inequivalent asymmetric

Ferrers graphs with 26 points.
1213 is the number of different

degree sequences for graphs with 8 vertices.
1214 is a number whose product of digits is equal to its sum of digits.

1215 is the smallest number n where n and n+1 are both products of 6 or more

primes.
1217 is a

Proth prime.
1219 is a number whose sum of

divisors is a 4^{th} power.
1220 is the number of labeled mappings from 5 points to themselves with exactly 2 cycles.

1221 = 1 × 11 × 111.

1222 is a

hexagonal pyramidal number.
1223 is the smallest number with

complexity 24.
1225 is the smallest number that can be written as the sum of 4

cubes in 3 ways.
1228 is a structured pentagonal hexacontahedral number.

1229 is the number of

primes less than 10000.
1230 is the number of

square-free graphs with 9 vertices.
1231 has the property that 1

^{7} + 2

^{7} + 3

^{7} + 1

^{7} = 1231

_{8}.

1232 = (7 × 8 × 9 × 10 × 11) / (7 + 8 + 9 + 10 + 11) .

1233 = 12

^{2} + 33

^{2}.

1234 is the smallest 4-digit number with increasing digits.

1236 is the number of

conjugacy classes of the alternating group A_{26}.
1237 is the smallest

prime that contains exactly 5 smaller primes as substrings.
1238 is the number of

rooted ternary trees with 11 vertices.
1239 is a value of n for which n

^{8}, n

^{9}, n

^{10}, and n

^{11} have the same digit sum.

1240 is the number of symmetric arrangements of 6 non-attacking

queens on a 6×6 chessboard.
1241 is a

centered cube number.
1243 is the number of essentially different ways to dissect a 18-gon into 8

quadrilaterals.
1245 is a dodecagonal pyramidal number.

1246 is the number of

partitions of 38 in which no part occurs only once.
1248 is the smallest number with the property that its first 6 multiples contain the digit 4.

1249 is the number of

simplicial polyhedra with 11 vertices.
1250 has a reciprocal that terminates in base 10.

1252 is the number of ways to tile a 4×24 rectangle with 4×1 rectangles.

1253 is a value of n for which

σ(n+1) = 2σ(n).
1254 is the number of

13-iamonds whose adjacency graph has a cycle.
1255 is a

Friedman number.
1257 is a value of n for which

φ(σ(n)) = φ(n).
1258 is the number of

commutative asymmetric semigroups of order 6.
1260 is the smallest number with 36

divisors.
1261 is a

Hexanacci-like number starting from 1, 1, 1, 1, 1, and 1.
1262 is the number of subsets of {1,2,3,...,14} that have a sum divisible by 13.

1265 has a 5

^{th} power that contains the same digits as 164

^{7}.

1271 has a 6

^{th} power whose last few digits are ...21211121.

1275 is the smallest number so that it and its neighbors are products of two

primes and the square of a prime.
1276 = 1111 + 22 + 77 + 66.

1278 has a

square root whose decimal part starts with the digits 1-9 in some order.
1279 is the exponent of a

Mersenne prime.
1280 is the number of tilted rectangles with vertices in a 10×10 grid.

1281 has the property that if each digit is replaced by its

square, the resulting number is a square.
1283 is the number of ways to divide a 8×8 grid of points into two sets using a straight line.

1285 is the number of

9-ominoes.
1287 =

_{13}C_{5}.
1288 is the number of possible positions in Othello after 2.5 moves.

1289 is a

truncated octahedral number.
1290 is the number of

connected graphs with 8 vertices and 16 edges.
1291 is the number of possible rows in a 16×16 crossword puzzle.

1292 is a factor of the sum of the digits of 1292

^{1292}.

1293 is a structured truncated tetrahedral number.

1294 is the number of 4 dimensional

polytopes with 8 vertices.
1295 = 5555 in base 6.

1296 is a

Friedman number.
1297 is a

Tetranacci-like number starting from 1, 1, 1, and 1.
1298 has a base 3 representation that ends with its base 6 representation.

1299 are the first 4 digits of 8

^{1299}.

1300 is the sum of the first four 5

^{th} powers.

1301 is the number of

trees with 13 vertices.
1302 is the number of

trees on 17 vertices with diameter 5.
1303 is the number of

multigraphs with 7 vertices and 8 edges.
1304 = 1304

_{6} + 1304

_{9}.

1305 is the number of

graphs with 11 vertices and 9 edges.
1306 = 1

^{1} + 3

^{2} + 0

^{3} + 6

^{4}.

1307 is a number n for which n

^{2}+1 is 7 times another square.

1308 is the smallest value of n for which n, n+1, n+2, and n+3 have the same number of

prime factors.
1309 is a member of the

Fibonacci-type sequence starting with 1 and 5.
1310 is the smallest number so that it and its neighbors are products of three distinct

primes.
1311 is the

trinomial coefficient T(19,16).
1314 divides the sum of the digits of 1314!.

1318 is the

rectilinear crossing number of complete graph K_{19}
1320 =

_{12}P_{3}.
1323 is an

Achilles number.
1324 is the

Entringer number E(7,5).
1325 is a

Markov number.
1327 is the smallest

prime for which the closest 6 primes are all smaller.
1328 and the following 32 numbers are

composite.
1330 =

_{21}C_{3}.
1331 is a

cube containing only odd digits.
1332 has a base 2 representation that begins and ends with its base 6 representation.

1333 has a base 2 representation that ends with its base 6 representation.

1334 is a value of n for which

σ(n) = σ(n+1).
1337 spells Leet in Leet.

1338 is a number n for which

φ(n) is a repdigit.
1340 has a

square with a digit sum larger than its 5^{th} power.
1341 is a number n for which

φ(n) is a repdigit.
1342 is the smallest number that is 15 away from a

prime.
1343 is the smallest number that is 16 away from a

prime.
1344 is the order of a

perfect group.
1345 is the number of

permutations of 8 elements that have 5^{th} power equal to the identity permutation.
1347 is the concatenation of the first 4

Lucas numbers.
1348 is the number of ways to stack 22 pennies in contiguous rows so that each penny lies on the table or on two pennies.

1349 is the maximum number of pieces a

torus can be cut into with 19 cuts.
1351 has the property that

e^{1351} is within .0009 of an integer.
1352 is an hexagonal prism number.

1353 is the ratio of

Fibonacci numbers.
1354 has a 5

^{th} power that is closer to a

cube than a square.
1356 is a truncated square pyramid number.

1357 has digits in

arithmetic sequence.
1358 is a value of n for which n

!!!! + 1 is prime.
1360 is the number of ways to place 3 non-attacking

knights on a 5×5 chessboard.
1361 is the index of a

prime Lucas number.
1362 is the smallest number that has a

square root whose decimal part starts with the digits 0-9 in some order.
1363 is a value of n for which

σ(φ(n)) = 2σ(n).
1364 is the 15

^{th} Lucas number.
1365 =

_{15}C_{4}.
1366 is the number of ways to place 28 points on a 14×14 grid so that

no 3 points are on a line.
1367 is the number of

anisohedral 18-iamonds.
1368 is the number of ways to fold a 3×3 rectangle of stamps.

1369 is a

square whose digits are non-decreasing.
1370 = 1

^{2} + 37

^{2} + 0

^{2}.

1371 = 1

^{2} + 37

^{2} + 1

^{2}.

1372 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with

integer dimensions less than 10.
1373 is the number of digits of the 17

^{th} perfect number.
1375 is a decagonal pyramidal number.

1376 is the smallest number with the property that it and its neighbors are not

cubefree.
1377 is the number of interior intersections when all the diagonals of a

regular 16-gon are drawn.
1378 is the number of

symmetric idempotent 6×6 matrices over GF(2).
1379 is the magic constant of a 24×24 magic square.

1380 is the number of intersections when all the diagonals of a

regular 15-gon are drawn.
1381 is the number of

anisohedral 17-ominoes.
1383 is the number of

anisohedral 13-hexes.
1384 has the same digits as the 1384

^{th} prime.
1385 is the 4

^{th} secant number.
1386 = 1 + 3

^{4} + 8 + 6

^{4}.

1387 divides the sum of the binary digits of 1387!.

1389 is the number of unit

interval graphs with 9 vertices.
1390 is the smallest number in base 6 to have 5 different digits.

1391 is the number of squares in a 10×10 grid of squares with diagonals drawn.

1392 is the number of

ternary square-free words of length 18.
1393 is an

NSW number.
1394 is the maximum number of regions space can be divided into by 17

spheres.
1395 is a

vampire number.
1399 is the number of subsets of {1,2,3,...,13} that have an

integer average.
1400 is the number of different arrangements of 4 non-attacking

queens on a 4×10 chessboard.
1405 is the sum of consecutive

squares in 2 ways.
1406 has a 4

^{th} root that starts 6.12345....

1408 is the number of

symmetric 3×3 matrices in base 4 with determinant 0.
1409 is the only positive number known whose 8

^{th} power can be written as the sum of eight 8

^{th} powers.

1410 is the number of

Ore graphs with 9 vertices.
1411 is the number of

quasi-groups of order 5.
1412 has a

cube whose digits occur with the same frequency.
1413 is the smallest number that can not be formed using the digits 0-7 at most once, together with the symbols + – × and ÷.

1414 is the smallest number whose

square contains 3 consecutive 9's.
1415 is a centered icosahedral number.

1416 is the number of connected planar maps with 6 edges.

1418 is the number of (not necessarily distinct) sets of

Egyptian fractions that sum to 1 with smallest fraction 1/18.
1419 is a

Zeisel number.
1420 +

σ(1420) = 4444.
1421 is a value of n for which

σ(φ(n)) = 2σ(n).
1422 is the number of ways to stack 27 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

1423 is the number of digits in the 3

^{rd} Cullen prime.
1426 is the number of

partitions of 42 into distinct parts.
1427 is the number of ways to write 23 as the ordered sum of positive squares.

1428 is the number of ways a 6×1 rectangle can be surrounded by 6×1 rectangles.

1429 is the smallest number whose

square has the first 3 digits the same as the next 3 digits.
1430 is the 8

^{th} Catalan number.
1432 is a

Padovan number.
1434 is a number whose sum of

squares of the divisors is a square.
1435 is a

vampire number.
1437 is the smallest number that can not be formed using the digit 1 at most 19 times, together with the symbols +, × and ^.

1438 is the smallest number with

complexity 25.
1439 is the smallest number with

complexity 26.
1440 = 2! × 3! × 5!.

1441 is a

palindrome in base 6 and in base 10.
1443 is a number n for which the sum of the first n

composite numbers is a palindrome.
1444 is a

square whose digits are non-decreasing.
1445 divides the sum of the binary digits of 1445!.

1446 is the number of

graphs with 9 vertices and 5 edges.
1448 is the number of

8-hexes.
1449 is a

stella octangula number.
1450 is the total number of

labeled graphs on 0-5 vertices.
1451 is the 5

^{th} central heptanomial coefficient.

1452 is a value of n so that n(n+4) is a

palindrome.
1453 is a member of the

Fibonacci-type sequence starting with 2 and 5.
1454 = 11 + 444 + 555 + 444.

1455 is the number of

subgroups of the symmetric group on 6 symbols.
1456 is the number of regions formed when all diagonals are drawn in a

regular 15-gon.
1457 is a number that does not have any digits in common with its

cube.
1458 is the maximum

determinant of a binary 11×11 matrix.
1459 is the sum of the

cubes of the digits of the sum of the cubes of its digits.
1460 is a value of n for which n

^{2} and n

^{3} use the same digits.

1464 = 1111 in base 11.

1465 has a

square that is formed by inserting three 2's into it.
1467 has the property that

e^{π√1467} is within 10^{-8} of an integer.
1468 is the smallest number whose 6

^{th} power has 20 digits.

1469 is the number of ways to play the first 4 moves in Checkers.

1470 is a

pentagonal pyramidal number.
1471 is the number of regions the

complex plane is cut into by drawing lines between all pairs of 15^{th} roots of unity.
1474 is a member of the

Fibonacci-type sequence starting with 2 and 9.
1475 is the maximum value of n so
that there exist 5 denominations of stamps so that every postage from 1
to n can be paid for with at most 11 stamps.

1476 is the number of

graphs with 9 edges.
1477 is a value of n for which n! + 1 is

prime.
1479 is the number of planar partitions of 12.

1480 is the number of asymmetric

trees with 19 vertices.
1481 is a number n for which n, n+2, n+6, and n+8 are all

prime.
1485 is the number of 3-colored

rooted trees with 5 vertices.
1486 is the number of different

score sequences of an 10-team round robin tournament.
1490 is the 14

^{th} Tetranacci number.
1491 has an 8

^{th} power whose first few digits are 24424244....

1492 is the number of lines passing through at least 2 points of an 9×9 grid of points.

1493 is the largest known

Stern prime.
1494 is the sum of its

proper divisors that contain the digit 4.
1496 is the sum of the first 16

squares.
1497 is a

Perrin number.
1498 is the number of inequivalent asymmetric

Ferrers graphs with 27 points.
1499 is a

prime that remains prime if any digit is deleted.
1500 = (5+1) × (5+5) × (5+0) × (5+0).

1503 is a

Friedman number.
1504 is the number of

anisohedral 21-iamonds.
1505 is the number of necklaces possible with 6 beads, each being one of 5 colors.

1506 is the sum of its

proper divisors that contain the digit 5.
1507 is the number of

partitions of 32 that do not contain 1 as a part.
1508 is a

heptagonal pyramidal number.
1512 is the number of inequivalent

Ferrers graphs with 27 points.
1514 is a number whose

square and cube use different digits.
1515 is the number of

trees on 15 vertices with diameter 6.
1517 is the product of two consecutive

primes.
1518 is the sum of its

proper divisors that contain the digit 5.
1520 is the smaller number in a

Ruth-Aaron pair.
1521 is the smallest number that can be written as the sum of 4 distinct

cubes in 3 ways.
1522 has the property that if each digit is replaced by its

square, the resulting number is a square.
1525 is a value of n for which

σ(φ(n)) = 2σ(n).
1526 is the number of

conjugacy classes of the alternating group A_{27}.
1529 is the number of (not necessarily distinct) sets of

Egyptian fractions that sum to 1 with smallest fraction 1/22.
1530 is a

vampire number.
1531 appears inside its 4

^{th} power.

1532 is the number of series-parallel networks with 9 unlabeled edges.

1533 is a

Kaprekar constant in base 2.
1534 = 4321 in base 7.

1535 is a

Thabit number.
1536 is not the sum of 4 non-zero

squares.
1537 has the property that dropping its first and last digits gives its largest

prime factor.
1538 does not occur in its

factorial in base 2.
1540 is a

tetrahedral triangular number.
1541 is a value of n for which

φ(n) = φ(n-1) + φ(n-2).
1542 are the first 4 digits of 2

^{1542}.

1543 = 1111 + 55 + 44 + 333.

1544 is the number of

connected 4-regular graphs with 12 vertices.
1545 is a cubic star number.

1546 is the number of 5×5 binary matrices with at most one 1 in each row and column.

1547 is a

hexagonal pyramidal number.
1549 is the smallest multi-digit number that is not the sum of a

prime and a non-trivial power.
1551 is the number of

trees on 25 vertices with diameter 4.
1552 has a sum of

prime factors that is equal to the sum of the prime factors of the two preceding numbers.
1553 is the number of polygons formed by 9 points on a circle, if adjacent points can not be joined.

1554 is the

trinomial coefficient T(9,3).
1555 is the largest n so that

**Q**(√n) has class number 4.
1556 is the sum of the

squares. of the first 9 primes.
1557 has a

square where the first 6 digits alternate.
1559 is the smallest

prime p with 16 consecutive quadratic residues mod p.
1560 is the maximum number of pieces a

torus can be cut into with 20 cuts.
1561 is the number of

series-reduced trees with 19 vertices.
1562 = 22222 in base 5.

1563 is the smallest number with the property that its first 4 multiples contain the digit 6.

1568 is the smallest

Rhonda number.
1569 is the number of labeled mappings from 5 points to themselves with exactly 1 cycles.

1571 is the smallest number that can not be formed using the digit 1 at most 23 times, together with the symbols +, –, × and ÷.

1573 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
1574 is the closest

integer to 15^{e}.
1575 is the number of

partitions of 24.
1577 divides 1

^{1} + 2

^{2} + 3

^{3} +

^{ . . .} + 1577

^{1577}.

1578 is the number of

Hamiltonian paths of a 3×8 rectangle graph.
1579 is the smallest

prime that remains prime when preceded and followed by one, two, three, or four 9's.
1581 is the smallest number whose 8

^{th} power contains exactly the same digits as another 8

^{th} power.

1582 is a value of n so that n(n+4) is a

palindrome.
1584 has a base 3 representation that ends with its base 6 representation.

1585 has a base 3 representation that ends with its base 6 representation.

1586 has a base 3 representation that ends with its base 6 representation.

1587 is a number that does not have any digits in common with its

cube.
1589 is the starting location of 7777 in the decimal expansion of

π.
1590 is the denominator of the 52

^{nd} Bernoulli number.
1591 is the sum of the first 13 numbers that have digit sum 13.

1592 is a number that does not have any digits in common with its

cube.
1593 has the property that dropping its first and last digits gives its largest

prime factor.
1595 is the smallest quasi-Carmichael number in base 2.

1596 is the sum of the first 15

Fibonacci numbers.
1597 is the 17

^{th} Fibonacci number.
1600 = 4444 in base 7.

1601 is the number of

forests with 12 vertices.
1605 is the number of 7-octs.

1606 is the number of

strongly connected digraphs with 4 vertices.
1609 is the smallest number whose

square contains 4 consecutive 8's.
1610 is the number of

partitions of 43 into distinct parts.
1613 is the index of a

prime Euclid number.
1614 is the number of arrangements of 5 non-attacking

queens on a 9×5 chessboard.
1617 is the maximum value of n so
that there exist 6 denominations of stamps so that every postage from 1
to n can be paid for with at most 9 stamps.

1618 has the property that the concatenation of its

prime factors in increasing order is a square.
1620 is a highly abundant number.

1621 is a

prime that remains prime when preceded and followed by one, two, three, or four 3's.
1624 is the

Stirling number of the first kind s(7,3).
1625 is the number of

circular permutations of a set with 8 elements with no element being mapped to its successor.
1626 is the number of binary

partitions of 31.
1627 is the smallest

prime so that it and the next 2 primes all end in 7.
1629 is an icosahedral number.

1630 is the number of

14-ominoes with a line of symmetry.
1631 is the number of ordered subsets of {1,2,3,4,5} than contain the number 1.

1632 is the smallest number with the property that its first 5 multiples contain the digit 6.

1633 is a number whose

square and cube use different digits.
1634 is a

narcissistic number.
1635 has a 5

^{th} root whose decimal part starts with the digits 1-9 in some order.

1636 appears inside its 4

^{th} power.

1637 is the number of

graphs with 9 vertices and 10 edges.
1638 is a

harmonic divisor number.
1639 is the number of

binary rooted trees with 16 vertices.
1640 = 2222 in base 9.

1641 has the property that if each digit is replaced by its

square, the resulting number is a square.
1643 = 31 × 53 = 3153

_{8}.

1648 is a

betrothed number.
1649 is a

Leyland number.
1650 is the number of connected

partial orders on 7 unlabeled elements.
1651 is the

trinomial coefficient T(13,9).
1652 is a member of the

Fibonacci-type sequence starting with 4 and 9.
1657 is a

Cuban prime.
1659 is a structured truncated octahedral number.

1661 is a centered dodecahedral number.

1663 is the number of

partitions of 41 in which no part occurs only once.
1664 is a value of n so that n(n+9) is a

palindrome.
1665 is the number of triangles of any size contained in the triangle of side 18 on a triangular grid.

1666 is the sum of the Roman numerals.

1667 +

φ(1667) = 3333.
1668 is the maximum number of regions space can be divided into by 18

spheres.
1669 is the smallest number whose 9

^{th} power has 29 digits.

1670 has a 6

^{th} root that starts 3.44444....

1671 divides the sum of the first 681

composite numbers.
1673 is a number with the property that the

root-mean-square of its divisors is an integer.
1674 is the smallest n for which Σ

_{k≤n} 1/k ≥ 8.

1675 has the property that dropping its first and last digits gives its largest

prime factor.
1676 = 1

^{1} + 6

^{2} + 7

^{3} + 6

^{4}.

1679 is the smallest multiple of 23 whose digits add to 23.

1680 is the smallest number with 40

divisors.
1681 is a

square and each of its two 2-digit parts is square.
1682 is the number of

monoids of order 7 with 7 idempotents.
1683 is a

Delannoy number.
1684 is the number of

multigraphs with 6 vertices and 9 edges.
1688 is a

truncated tetrahedral number.
1689 is the smallest

composite number all of whose proper divisors contain the digit 9.
1690 is the number of ordered sequences of coins totaling 27 cents.

1691 is the number of

multigraphs with 5 vertices and 11 edges.
1692 has a

square with the first 3 digits the same as the next 3 digits.
1694 has a

cube whose digits occur with the same frequency.
1695 is a

rhombic dodecahedral number.
1696 is the number of regions formed when all diagonals are drawn in a

regular 16-gon.
1697 is the smallest

prime factor of 26! + 1.
1700 is the

generalized Catalan number C(13,4).
1701 is the

Stirling number of the second kind S(8,4).
1702 has a

square that contains the same digits as 13^{6}.
1705 is the smallest quasi-Carmichael number in base 4.

1706 = 5 × 6 × 7 × 8 + 5 + 6 + 7 + 8.

1708 is the number of permutations s of {1,2,3,4,5,6,7,8} for which | s(i)-i | > 1 for all i.

1709 is the index of a

Wagstaff prime.
1710 is the smallest non-

palindrome where it and its reverse are divisible by 19.
1711 is a

triangular number that is the product of two primes.
1712 is the number of regions the

complex plane is cut into by drawing lines between all pairs of 16^{th} roots of unity.
1713 is the number of

14-iamonds with holes.
1714 is the number of

graphs with 9 vertices and 7 cycles.
1715 = 1 × 7

^{3} × 1 × 5.

1716 =

_{13}C_{6}.
1722 is a

Giuga number.
1724 is the number of

matroids on 8 points.
1725 is a structured deltoidal hexacontahedral number.

1727 and its reverse are both differences of positive

cubes.
1728 = 12

^{3}.

1729 is a

taxicab number.
1730 is the sum of consecutive

squares in 2 ways.
1731 is the sum of the

squares of 3 consecutive primes.
1733 is the smallest

prime that contains exactly 6 smaller primes as substrings.
1734 is the sum of its

proper divisors that contain the digit 8.
1736 is the number of ways to place 2 non-attacking

bishops on a 8×8 chessboard.
1737 is a value of n so that (n-1)

^{2} + n

^{2} + (n+1)

^{2} is a

palindrome.
1738 = 6952 / 4, and this equation uses each digit 1-9 exactly once.

1739 is a value of n for which n

^{8}, n

^{9}, n

^{10}, and n

^{11} have the same digit sum.

1740 has a base 5 representation that begins with its base 9 representation.

1741 is the smallest

prime so that it and the next 5 primes are all equal to 1 (mod 6).
1747 is a value of n for which n (n+2) is a

palindrome.
1749 is the number of digits in the 4

^{th} Cullen prime.
1751 is the 6

^{th} central pentanomial coefficient.

1753 is the largest

prime factor of 8! - 1.
1755 = 3333 in base 8.

1756 is the number of ways to stack 28 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

1757 is the smallest multi-digit number n, that when interpreted in base 17, gives a multiple of n.

1759 is an Eisenstein-Mersenne prime.

1763 is the product of

twin primes.
1764 is the

Stirling number of the first kind s(7,2).
1769 is the 4-digit string that appears latest in the decimal expansion of

e.
1770 is the number of

conjugacy classes in the automorphism group of the 13 dimensional hypercube.
1771 is a tetrahedral

palindrome.
1775 is a member of the

Fibonacci-type sequence starting with 1 and 7.
1778 is the largest number whose

square has 5 digits.
1779 is the smallest number whose 4

^{th} power has 13 digits.

1780 is a structured truncated tetrahedral number.

1782 is the smallest number n that is 3 times the sum of all the 2-digit numbers that can be made using the digits of n.

1784 is a number n for which

φ(n) is a repdigit.
1785 is a

Kaprekar constant in base 2.
1786 has a

cube that contains only digits 5 and larger.
1787 is the number of different arrangements (up to rotation and reflection) of 12 non-attacking

queens on a 12×12 chessboard.
1789 is the smallest number with the property that its first 4 multiples contain the digit 7.

1792 is a

Friedman number.
1793 is a

Pentanacci number.
1794 has a base 5 representation that begins with its base 9 representation.

1795 has a base 5 representation that begins with its base 9 representation.

1798 is a value of n for which

φ(σ(n)) = φ(n).
1799 is the sum of the

cubes of 3 consecutive primes.
1800 is a

pentagonal pyramidal number.
1801 is a

Cuban prime.
1804 is the number of 3×3 sliding puzzle positions that require exactly 14 moves to solve starting with the hole on a side.

1805 has the property that if each digit is replaced by its

square, the resulting number is a square.
1806 is a

Schröder number.
1807 is a member of

Sylvester's sequence.
1812 is the number of

fullerenes with 60 carbon atoms.
1813 is the number of

trees on 15 vertices with diameter 8.
1815 has a 4

^{th} power in base 7 with no isolated digits.

1816 is the number of

partitions of 44 into distinct parts.
1817 is the number of

polyominoes with 8 or fewer squares.
1818 evenly divides the sum of its rotations.

1819 has a 7

^{th} power that contains the same digits as 322

^{9}.

1820 =

_{16}C_{4}.
1822 has a

cube that contains only even digits.
1823 has a

square with the first 3 digits the same as the next 3 digits.
1824 has a

cube that contains only even digits.
1825 is the smallest number whose

square begins with three 3's.
1826 has the property that the sum of its

prime factors is equal to the product of its digits.
1827 is a

vampire number.
1828 is the 6

^{th} meandric number and the 11^{th} open meandric number.
1830 is the number of

ternary square-free words of length 19.
1831 is the smallest

prime that is followed by 15 composite numbers.
1834 is an

octahedral number.
1835 is the number of Pyramorphix puzzle positions that require exactly 4 moves to solve.

1836 has a 4

^{th} power whose product of digits is also a 4

^{th} power.

1837 is a value of n for which 2n and 7n together use the digits 1-9 exactly once.

1840 are the first 4 digits of 1

^{1} + 2

^{2} + 3

^{3} +

^{ . . .} + 1840

^{1840}.

1842 is the number of

rooted trees with 11 vertices.
1843 has a

square root whose decimal part starts with the digits 0-9 in some order.
1847 is the number of 2×2×2

Rubik's cube positions that require exactly 4 moves to solve.
1848 is the smallest value of n for which

_{2n}C_{n} is divisible by n^{2}.
1849 is the smallest

composite number all of whose proper divisors contain the digit 4.
1850 = (10

^{3} + 10

^{4} + 10

^{5}) / (3 × 4 × 5).

1851 is the number of inequivalent asymmetric

Ferrers graphs with 28 points.
1854 is the number of

derangements of 7 items.
1855 is the number of

permutations of 7 items that fix 1 element.
1858 is the number of isomers of C

_{14}H

_{30}.

1860 is the number of ways to 12-color the faces of a

tetrahedron.
1862 is the number of Chess positions that can be reached in only one way after 2 moves by white and 1 move by black.

1863 is the larger number in a

Ruth-Aaron pair.
1865 = 12345 in base 6.

1866 is the number of inequivalent

Ferrers graphs with 28 points.
1868 is the smallest number that can not be formed using the digit 1 at most 20 times, together with the symbols +, × and ^.

1869 is the closest

integer to 11^{π}.
1870 is the product of two consecutive

Fibonacci numbers.
1871 is a number n for which n, n+2, n+6, and n+8 are all

prime.
1873 is a value of n for which one less than the product of the first n

primes is prime.
1875 is the smallest order for which there are 21

groups.
1876 is the closest

integer to 16^{e}.
1880 is a number whose sum of

squares of the divisors is a square.
1883 is the number of

conjugacy classes of the alternating group A_{28}.
1885 is a

Zeisel number.
1889 is the smallest

prime so that it and the next 4 primes are all equal to 5 (mod 6).
1890 is the number of

permutations of 10 items that fix 6 elements.
1891 is a

triangular number that is the product of two primes.
1893 is the number of 3×3 sliding puzzle positions that require exactly 14 moves to solve starting with the hole in a corner.

1894 = 1

^{4} 2

^{3} 3

^{2} 4

^{1}
1895 is a value of n for which n, 2n, 3n, 4n, 5n, and 6n all use the same number of digits in

Roman numerals.
1896 is the number of

graphs with 9 vertices with clique number 2.
1897 is a

Padovan number.
1898 is a value of n for which

σ(n) = φ(n) + φ(n-1) + φ(n-2).
1900 is the largest

palindrome in Roman numerals.
1902 has a

cube that contains only even digits.
1903 is the smallest number requiring an

addition chain of length 15.
1905 is a

Kaprekar constant in base 2.
1907 is a value of n for which n (n+2) is a

palindrome.
1908 is the number of self-dual

planar graphs with 22 edges.
1911 is a

heptagonal pyramidal number.
1912 is a structured octagonal anti-diamond number.

1913 is

prime and contains the same digits as the next prime.
1915 is the number of

semigroups of order 5.
1916 is the number of ways to tile a 6×5 rectangle with

integer-sided squares.
1917 is the number of possible configurations of pegs (up to symmetry) after 27 jumps in solitaire.

1919 is a member of the

Fibonacci-type sequence starting with 2 and 7.
1920 is the smallest number that contains more different digits than its

cube.
1921 has a sum of

prime factors that is equal to the sum of the prime factors of the two preceding numbers.
1923 is the smallest number whose

cube contains 5 consecutive 1's.
1925 is a

hexagonal pyramidal number.
1931 is the smallest number whose 7

^{th} power has 23 digits.

1932 is 1/23 of the 23

^{rd} Fibonacci number.
1933 is a

prime factor of 111111111111111111111.
1934 is the smallest number so that it and the next 11 numbers all have an even number of

prime factors.
1935 is the maximum value of n so
that there exist 4 denominations of stamps so that every postage from 1
to n can be paid for with at most 17 stamps.

1936 is a

Hexanacci number.
1937 is the number of digits of the 18

^{th} perfect number.
1941 is the maximum number of regions a circle can be cut into by joining 15 points on the circumference with straight lines.

1942 is the smallest number whose

cube contains 5 consecutive 8's.
1944 is a member of the

Fibonacci-like multiplication series starting with 2 and 3.
1945 is the number of triangles of any size contained in the triangle of side 19 on a triangular grid.

1947 is the number of

planar partitions of 16.
1948 is the number of 4×4 sliding puzzle positions that require exactly 10 moves to solve starting with the hole in a corner.

1950 = (144 + 145 + . . . + 156) = (157 + 158 + . . . + 168).

1952 + 2 is the sum of the

proper divisors of 1952.
1953 is a

Kaprekar constant in base 2.
1954 is the number of subsets of {1, 2, 3, ... 16} that do not contain solutions to x + y = z.

1956 is the number of ways to color the vertices of a triangle with 18 colors, up to rotation.

1957 is the number of

permutations of some subset of 6 elements.
1958 is the number of

partitions of 25.
1959 is a

Lucas 7-step number.
1960 is the

Stirling number of the first kind s(8,5).
1961 is a

strobogrammatic number.
1962 is the smallest value of n for which 2n and 9n together use the digits 1-9 exactly once.

1963 = 7852 / 4, and this equation uses each digit 1-9 exactly once.

1964 is the number of legal knight moves in Chess.

1966 has a

cube that contains only digits 5 and larger.
1969 is the only known counterexample to a conjecture about modular

Ackermann functions.
1973 has a 4

^{th} power that is 1/2 of the sum of three 4

^{th} powers.

1976 is the maximum number of regions space can be divided into by 19

spheres.
1979 has a 6

^{th} root whose decimal part starts with the digits 1-9 in some order.

1980 is the number of ways to fold a 2×4 rectangle of stamps.

1983 is a

Perrin number.
1990 is a

stella octangula number.
1991 are the first 4 digits of 6

^{1991}.

1994 is the number of digits in the 5

^{th} Cullen prime.
1995 is the number of

graphs with 9 vertices with clique number 6.
1997 is a

prime factor of 87654321.
1998 is the largest number that is the sum of its digits and the

cube of its digits.
1999 is the smallest number whose digits add to 28.

2000 = 5555 in base 7.

2001 has a

square with the first 3 digits the same as the next 3 digits.
2002 =

_{14}C_{5}.
2003 is a

Lucas 8-step number.
2004 has a

square with the last 3 digits the same as the 3 digits before that.
2007 divides the sum of the digits of 2

^{2007} × 2007!.

2008 is a

Kaprekar constant in base 3.
2009 ! ends in exactly 500 zeros.

2010 is the number of

trees on 15 vertices with diameter 7.
2015 is a

Lucas-Carmichael number.
2016 is a value of n for which n

^{2} + n

^{3} contains one of each digit.

2017 is a value of n for which

φ(n) = φ(n-1) + φ(n-2).
2020 is an autobiographical number.

2021 is the product of two consecutive

primes.
2024 =

_{24}C_{3}.
2025 is a

square that remains square if all its digits are incremented.
2028 is the number of

graphs with 9 vertices that have chromatic number 6.
2029 is an Eisenstein-Mersenne prime.

2030 is the smallest number that can be written as a sum of 3 or 4 consecutive

squares.
2034 is the number of

self-avoiding walks of length 9.
2036 is the number of ways 11 people can line up so that only one person has a taller person in front of him.

2037 is a truncated cube number.

2038 is the number of

Eulerian graphs with 9 vertices.
2039 is the smallest prime that contains ten 1's in binary.

2040 = 2040

_{5} + 2040

_{7} + 2040

_{8}.

2041 is a

12-hyperperfect number.
2044 is the number of rectangles with corners on an 9×9 grid of points.

2045 is the number of unlabeled

partially ordered sets of 7 elements.
2046 is the maximum number of pieces a

torus can be cut into with 22 cuts.
2047 is the smallest

composite Mersenne number with prime exponent.
2048 is the smallest non-trivial 11

^{th} power.

2049 is a

Cullen number.
2050 is the number of subsets of the 22

^{nd} roots of unity that add to 0.
2052 is the magic constant for a 8×8×8

magic cube.
2053 is a value of n for which one less than the product of the first n

primes is prime.
2054 is the number of subsets of the 33

^{rd} roots of unity that add to 0.
2055 is the

rectilinear crossing number of complete graph K_{21}
2056 is the magic constant of a 16×16 magic square.

2057 is a centered icosahedral number.

2058 is the number of

integers with complexity 27.
2059 is a centered tetrahedral number.

2061 is the number of sets of distinct positive

integers with mean 7.
2063 is a member of the

Fibonacci-type sequence starting with 3 and 7.
2067 is a value of n so that n(n+5) is a

palindrome.
2072 is the smallest number that can be written in exactly 6 ways as the sum of a number and the product of its non-zero digits.

2073 is a

Genocchi number.
2074 is the smallest number that can not be formed using the digit 1 at most 24 times, together with the symbols +, –, × and ÷.

2075 is the number of

connected graphs with 9 vertices and 11 edges.
2076 is a value of n for which n

!!! + 1 is prime.
2078 has a

cube whose digits occur with the same frequency.
2080 is the number of different arrangements (up to rotation and reflection) of 26 non-attacking

bishops on a 14×14 chessboard.
2081 is a number n for which n, n+2, n+6, and n+8 are all

prime.
2082 is the sum of its

proper divisors that contain the digit 4.
2086 is a number n for which

φ(n) is a repdigit.
2089 is the smallest number that ends an arithmetic progression of 10 numbers with the same

prime signature.
2090 is the number of possible rows in a 17×17 crossword puzzle.

2100 is divisible by its reverse.

2101 = 2101

_{5} + 2101

_{7} + 2101

_{8}.

2108 does not occur in its

factorial in base 2.
2109 is a value of n so that n(n+7) is a

palindrome.
2110 is a value of n for which reverse(

φ(n)) = φ(reverse(n)).
2112 is the number of subsets of {1, 1/2, 1/3, ... 1/36} that sum to an

integer.
2113 is a

Proth prime.
2114 is a number whose product of digits is equal to its sum of digits.

2116 has a base 10 representation which is the reverse of its base 7 representation.

2118 is a member of the

Fibonacci-type sequence starting with 1 and 5.
2119 is a value of n for which |cos(n)| is smaller than any previous

integer.
2120 is the number of ways to stack 16 pennies in a line so that each penny lies on the table or on two pennies.

2122 is the index of a

prime Euclid number.
2126 is a value of n so that n(n+3) is a

palindrome.
2127 is not the sum of a

square, a cube, a 4^{th} power, and a 5^{th} power.
2128 is the 7

^{th} central quadrinomial coefficient.

2130 and its reverse are both the averages of

twin primes.
2131 is the number of domino tilings of a 3×12 rectangle.

2132 is the maximum number of 11

^{th} powers needed to sum to any number.

2133 is a

2-hyperperfect number.
2135 is a value of n for which

σ(n-1) + σ(n+1) = σ(2n).
2136 is the number of different

degree sequences possible for a graph with 15 edges.
2137 does not occur in its

factorial in base 2.
2138 does not occur in its

factorial in base 2.
2140 is a cubic star number.

2141 is a number whose product of digits is equal to its sum of digits.

2143 is the number of

commutative semigroups of order 6.
2146 is a value of n for which 2

φ(n) = φ(n+1).
2147 has a

square with the last 3 digits the same as the 3 digits before that.
2148 is the number of

15-ominoes with a horizontal or vertical line of symmetry.
2150 divides the sum of the largest

prime factors of the first 2150 positive integers.
2155 is the smallest number whose

cube has 10 digits.
2156 is the number of different positions in Connect Four after 5 moves.

2158 is a number n for which n

^{2}+1 is 6 times another square.

2160 is the order of a

perfect group.
2161 is a

prime factor of 111111111111111111111111111111.
2163 are the first 4 digits of

π^{2163}.
2164 is the smallest number whose 7

^{th} power starts with 5 identical digits.

2167 is the number of

partitions of 34 that do not contain 1 as a part.
2168 is a structured hexagonal diamond number.

2169 is a

Leyland number.
2176 is the number of

prime knots with 12 crossings.
2178 is the only number known which when multiplied by its reverse yields a 4

^{th} power.

2179 is a

Wedderburn-Etherington number.
2182 is the number of degree 15

irreducible polynomials over GF(2).
2184 is the product of three consecutive

Fibonacci numbers.
2185 is the number of digits of 5

^{55}.

2186 = 2222222 in base 3.

2187 is a strong

Friedman number.
2188 is the 10

^{th} Motzkin number.
2192 is the number of necklaces (that can't be turned over) possible with 15 beads, each being one of 2 colors.

2194 is the number of

partitions of 42 in which no part occurs only once.
2195 is the number of necklaces with 9 beads, each one of 3 colors.

2196 is the only number n so that 2n, 3n, 7n, and 9n together contain every digit 1-9 exactly twice.

2197 = 13

^{3}.

2199 is a

perfect totient number.
2201 is the only non-

palindrome known to have a palindromic cube.
2202 is a factor of the sum of the digits of 2202

^{2202}.

2203 is the exponent of a

Mersenne prime.
2204 has the property that the sum of the

factorials of its digits is its largest prime factor.
2205 is an odd

primitive abundant number.
2207 is the 16

^{th} Lucas number.
2208 is a

Keith number.
2209 is a

Tribonacci-like number starting from 1, 1, and 1.
2210 =

_{47}C_{2} + _{47}C_{2} + _{47}C_{1} + _{47}C_{0}.
2211 is a

triangular number whose internal digits are triangular and whose external digits are triangular.
2212 is the closest

integer to 17^{e}.
2213 = 2

^{3} + 2

^{3} + 13

^{3}.

2217 has a base 2 representation that begins with its base 3 representation.

2219 is the number of

14-hexes with reflectional symmetry.
2221 is a value of n for which

σ(n) is a repdigit.
2222 is the smallest number divisible by a 1-digit

prime, a 2-digit prime, and a 3-digit prime.
2223 is a

Kaprekar number.
2225 has the property that the sum of the n

^{th} powers of its digits is prime for 1 ≤ n &\le 9.

2226 is the smallest number whose

cube contains 4 consecutive 9's.
2228 is the number of congruency classes of triangles with vertices from a 11×11 grid of points.

2230 is a number n for which

φ(n) is a repdigit.
2234 is the number of ways to stack 24 pennies in contiguous rows so that each penny lies on the table or on two pennies.

2235 is a value of n so that n(n+8) is a

palindrome.
2239 is a

prime that remains prime if any digit is deleted.
2240 is the number of unsymmetrical ways to dissect a

regular 13-gon into 11 triangles.
2241 is the sum of 3 consecutive

cubes.
2243 is the smallest

prime so that it and the next 2 primes are all equal to 3 (mod 8).
2244 is the

generalized Catalan number C(14,4).
2245 is the number of ways to tile a 8×4 rectangle with 2×1 rectangles.

2250 is the number of necklaces possible with 16 beads, each being one of 2 colors.

2252 is a

Franel number.
2253 is the number of

monic polynomials of degree 11 with integer coefficients whose complex roots are all in the unit disk.
2255 is the number of triangles of any size contained in the triangle of side 20 on a triangular grid.

2257 = 4321 in base 8.

2258 is the number of

anisohedral 16-ominoes.
2260 is an icosahedral number.

2261 = 2222 + 22 + 6 + 11.

2263 = 2222 + 2 + 6 + 33.

2264 is the number of

graphs with 8 vertices that have 4 automorphisms.
2266 is a dodecagonal pyramidal number.

2268 is the number of binary

partitions of 34.
2269 is a

Cuban prime.
2272 is the number of

graphs on 7 vertices with no isolated vertices.
2273 is the number of

functional graphs on 10 vertices.
2274 is the sum of its

proper divisors that contain the digit 7.
2275 is the sum of the first six 4

^{th} powers.

2277 is the

trinomial coefficient T(11,6).
2281 is the exponent of a

Mersenne prime.
2282 is the number of ways, up to rotation and reflection, of dissecting a

regular 13-gon into 11 triangles.
2284 is the number of 7-digit perfect powers.

2285 is a non-

palindrome with a palindromic square.
2291 is the number of inequivalent

Ferrers graphs with 29 points.
2292 is a

narcissistic number in base 6.
2293 is a

prime that remains prime if any digit is deleted.
2295 is the smallest number so that it and its successor are both the product of 2

primes and the cube of a prime.
2296 is a structured great rhombicubeoctahedral number.

2297 is the number of inequivalent binary

linear codes of length 10.
2299 is the number of ordered sequences of coins totaling 28 cents.

2300 =

_{25}C_{3}.
2303 is a number whose

square and cube use different digits.
2304 is the number of edges in a 9 dimensional

hypercube.
2305 has a base 6 representation that ends with its base 8 representation.

2306 has a base 6 representation that ends with its base 8 representation.

2307 has a base 6 representation that ends with its base 8 representation.

2308 is the number of

conjugacy classes of the alternating group A_{29}.
2309 is the largest

prime factor of 2 × 3 × 5 × 7 × 11 - 1.
2310 is the product of the first 5

primes.
2311 is a

Euclid number.
2312 is the number of

series-reduced planted trees with 10 leaves.
2316 = 1

^{7} + 2

^{7} + 3

^{7}.

2318 is the number of

connected planar graphs with 10 edges.
2320 is the maximum number of regions space can be divided into by 20

spheres.
2321 is a

Huay rhombic dodecahedral number.
2322 is the number of

connected graphs with 10 edges.
2323 is the maximum number of pieces a

torus can be cut into with 23 cuts.
2324 is a

narcissistic number in base 6.
2325 is the maximum number of regions a

cube can be cut into with 24 cuts.
2326 is the smallest number whose

cube contains every digit at least once.
2328 is the number of

groups of order 128.
2331 is a

centered cube number.
2333 is a

right-truncatable prime.
2336 is the number of sided

11-iamonds.
2339 is the number of ways to tile a 6×10 rectangle with the

pentominoes.
2340 = 4444 in base 8.

2342 is the number of subsets of {1,2,3,...,15} that have a sum divisible by 14.

2343 = 33333 in base 5.

2344 is the number of necklaces with 7 beads, each one of 4 colors.

2345 has digits in

arithmetic sequence.
2349 is a

Friedman number.
2350 is the number of quasi-

triominoes that fit inside a 11×11 grid.
2351 is a member of the

Fibonacci-type sequence starting with 2 and 5.
2352 does not occur in its

factorial in base 2.
2353 has the property that 588

^{2} + 2353

^{2} = 5882353 and 9412

^{2} + 2353

^{2} = 94122353.

2354 = 2222 + 33 + 55 + 44.

2357 is a

SmarandacheÐWellin prime.
2359 = 2222 + 33 + 5 + 99.

2360 is a

hexagonal pyramidal number.
2363 does not occur in its

factorial in base 2.
2365 is a value of n for which n (n+2) is a

palindrome.
2366 is the number of ways to legally add 2 sets of parentheses to a product of 12 variables.

2368 is the number of 3×3 sliding puzzle positions that require exactly 14 moves to solve starting with the hole in the center.

2371 is the number of ways a 7×1 rectangle can be surrounded by 7×1 rectangles.

2372 is the smallest number whose 8

^{th} power has 27 digits.

2376 is a structured truncated tetrahedral number.

2377 is a value of n for which one less than the product of the first n

primes is prime.
2378 is the 10

^{th} Pell number.
2380 =

_{17}C_{4}.
2385 is the smallest number whose 7

^{th} power contains exactly the same digits as another 7

^{th} power.

2387 is a structured rhombic triacontahedral number.

2388 is the number of

3-connected graphs with 8 vertices.
2391 is the number of ways to flip a coin 12 times and get at least 3 heads in a row.

2393 is a

right-truncatable prime.
2394 is the smallest value of n for which n and 7n together use each digit 1-9 exactly once.

2397 is the number of intersections when all the diagonals of a

regular 17-gon are drawn.
2398 is the number of 3×3 sliding puzzle positions that require exactly 28 moves to solve starting with the hole in the center.

2399 is a

right-truncatable prime.
2400 = 6666 in base 7.

2401 is the 4

^{th} power of the sum of its digits.

2402 has a base 2 representation that begins with its base 7 representation.

2405 has the property that if each digit is replaced by its

square, the resulting number is a square.
2406 is a

truncated octahedral number.
2407 is a value of n for which

σ(φ(n)) = 2σ(n).
2410 is the number of

3-valent trees with 16 vertices.
2411 is a number whose product of digits is equal to its sum of digits.

2414 is the number of symmetric

plane partitions of 28.
2417 has a base 3 representation that begins with its base 7 representation.

2420 is the number of possible rook moves on a 11×11 chessboard.

2424 has a

cube that contains the digits 2424 in reverse order.
2427 = 2

^{1} + 4

^{2} + 2

^{3} + 7

^{4}.

2430 is the number of unordered ways to write 1 as a sum of reciprocals of

integers no larger than 18.
2431 is the

Stirling number of the second kind S(13,11).
2432 does not occur in its

factorial in base 2.
2434 is the number of legal king moves in Chess.

2436 is the number of

partitions of 26.
2445 is a

truncated tetrahedral number.
2448 is the order of a

non-cyclic simple group.
2450 has a base 3 representation that begins with its base 7 representation.

2457 = 169 + 170 + . . . + 182 = 183 + 184 + . . . + 195.

2460 = 3333 in base 9.

2464 is the number of

permutations of 8 items that fix 3 elements.
2465 is a

Carmichael number.
2466 is the number of regions formed when all diagonals are drawn in a

regular 18-gon.
2467 has a

square with the first 3 digits the same as the next 3 digits.
2468 = 2 + 22 + 222 + 2222.

2469 is the smallest value of n for which 4n and 5n together use the digits 1-9 exactly once.

2470 is the sum of the first 19

squares.
2471 is the smallest number that can not be formed using the numbers 2

^{0}, 2

^{1}, ... , 2

^{6}, together with the symbols +, –, × and ÷.

2474 is a value of n for which |cos(n)| is smaller than any previous

integer.
2477 would be

prime if preceded and followed by a 1, 3, 7, or 9.
2478 is the number of

anisohedral 20-iamonds.
2484 is the number of regions the

complex plane is cut into by drawing lines between all pairs of 18^{th} roots of unity.
2485 is the number of planar partitions of 13.

2487 has a 4

^{th} power that is the sum of four 4

^{th} powers.

2491 is the product of two consecutive

primes.
2495 is the number of

13-iamonds that tile the plane.
2496 is the number of

3-connected planar maps with 17 edges.
2498 shares 3 consecutive digits with one of its

prime factors.
2499 has a

square root that starts 49.989998999....
2500 is a

Tetranacci-like number starting from 1, 1, 1, and 1.
2501 is a

Friedman number.
2502 is a strong

Friedman number.
2503 is a

Friedman number.
2504 is a

Friedman number.
2505 is a

Friedman number.
2506 is a

Friedman number.
2507 is a

Friedman number.
2508 is a

Friedman number.
2509 is a

Friedman number.
2510 is the maximum value of n so
that there exist 6 denominations of stamps so that every postage from 1
to n can be paid for with at most 10 stamps.

2511 is the smallest number so that it and its successor are both the product of a

prime and the 4^{th} power of a prime.
2512 is the smallest number whose 5

^{th} power has 17 digits.

2513 is a

Padovan number.
2515 is the number of symmetric 9-cubes.

2517 is the number of regions the

complex plane is cut into by drawing lines between all pairs of 17^{th} roots of unity.
2518 uses the same digits as

φ(2518).
2519 is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 12.

2520 is the smallest number divisible by 1 through 10.

2522 is the number of subsets of {1,2,3,...,15} that have a sum divisible by 13.

2524 and the two numbers before it and after it are all products of exactly 3

primes.
2525 and the two numbers before it and after it are all products of exactly 3

primes.
2528 is a structured truncated octahedral number.

2530 is a

Leyland number.
2532 = 2222 + 55 + 33 + 222.

2535 is the number of ways to 13-color the faces of a

tetrahedron.
2538 has a

square with 5/7 of the digits are the same.
2540 has a

square root whose decimal part starts with the digits 0-9 in some order.
2542 is the number of stretched

9-ominoes.
2545 = 2545

_{6} + 2545

_{9}.

2548 is the

generalized Catalan number C(11,5).
2550 is a

Kaprekar constant in base 4.
2557 is the number of

proper divisors of the 15^{th} perfect number.
2558 is the number of

divisors of the 15^{th} perfect number.
2560 is the number of 2×2

singular matrices mod 8.
2561 is the number of digits of the 19

^{th} perfect number.
2562 is a structured pentakis dodecahedral number.

2570 is the number of subsets of {1,2,3,...,14} that have an

integer average.
2571 is the smallest number with the property that its first 7 multiples contain the digit 1.

2573 is the number of

partitions of 35 that do not contain 1 as a part.
2574 is a value of n for which

_{2n}C_{n} is divisible by n^{2}.
2576 has exactly the same digits in 3 different bases.

2580 is a

Keith number.
2581 is the smallest number whose

square begins with three 6's.
2582 is the smallest number whose

square begins with four 6's.
2583 is the sum of the first 16

Fibonacci numbers.
2584 is the 18

^{th} Fibonacci number .
2585 is a truncated square pyramid number.

2587 is a value of n for which

φ(n) + φ(n+1) divides σ(n) + σ(n+1).
2590 is the number of

partitions of 47 into distinct parts.
2592 = 2

^{5} 9

^{2}.

2593 has a base 3 representation that ends with its base 6 representation.

2594 has a base 3 representation that ends with its base 6 representation.

2596 is the number of triangles of any size contained in the triangle of side 21 on a triangular grid.

2600 =

_{26}C_{3}.
2601 is a

pentagonal pyramidal number.
2606 is the number of

polyhedra with 9 vertices.
2609 is the number of

perfect squared rectangles of order 15.
2614 is the smallest value of n for which

π(9n) = n.
2615 is the number of functions from 9 unlabeled points to themselves.

2616 is the number of

graphs with 9 vertices and 6 cycles.
2617 is the index of a

Wagstaff prime.
2618 has a sum of digits equal to its largest

prime factor.
2620 is an

amicable number.
2621 = 2222 + 66 + 222 + 111.

2622 is a value of n for which 7n and 8n together use each digit exactly once.

2623 = 2222 + 66 + 2 + 333.

2624 is the maximum number of pieces a

torus can be cut into with 24 cuts.
2625 is a centered octahedral number.

2626 is the maximum number of regions a

cube can be cut into with 25 cuts.
2627 is a

Perrin number.
2629 is the smallest number whose

reciprocal has period 14.
2631 is a

Lucas 4-step number.
2632 has the same digits as the 2632

^{nd} prime.
2635 is the number of necklaces with 6 beads, each one of 5 colors.

2636 is a non-

palindrome with a palindromic square.
2637 is the number of

commutative monoids of order 7.
2639 is an enneagonal pyramidal number.

2641 is the

pseudosquare modulo 11.
2642 = 5

^{2} + 6

^{3} + 7

^{4}.

2646 is the

Stirling number of the second kind S(9,6).
2647 is the index of a

prime Euclid number.
2651 is the number of asymmetric

trees with 12 vertices.
2652 is the 9

^{th} super-ballot number.

2657 is a value of n for which one more than the product of the first n

primes is prime.
2659 is the maximum value of n so
that there exist 5 denominations of stamps so that every postage from 1
to n can be paid for with at most 13 stamps.

2662 is a

palindrome and the 2662^{nd} triangular number is a palindrome.
2663 is the number of digits of the 20

^{th} perfect number.
2664 is the smallest value of n for which n, n+1, n+2, n+3, and n+4 have the same number of

prime factors.
2665 is the number of

conjugacy classes in the automorphism group of the 14 dimensional hypercube.
2667 is a number whose sum of

divisors is a 6^{th} power.
2668 is the number of lines through exactly 2 points of a 11×11 grid of points.

2671 is a value of n for which 2n and 7n together use the digits 1-9 exactly once.

2672 and its successor are both divisible by 4

^{th} powers.

2673 is the largest number known that does not have any digits in common with its 4

^{th} power.

2676 is a number n for which

φ(n) is a repdigit.
2678 is the number of

connected graphs with 10 vertices and 11 edges.
2680 is the number of different arrangements of 11 non-attacking

queens on an 11×11 chessboard.
2682 is a number n for which

φ(n) is a repdigit.
2683 is the largest n so that

**Q**(√n) has class number 5.
2685 is a value of n for which

σ(n) = σ(n+1).
2688 is the order of a

perfect group.
2689 is a

Proth prime.
2690 is the number of terms in the 9

^{th} derivative of f(f(f(f(f(x))))).

2692 is the sum of the

squares of 4 consecutive primes.
2694 is the number of ways 22 people around a round table can shake hands in a non-crossing way, up to rotation.

2697 is the smallest value of n for which n and 5n together use each digit 1-9 exactly once.

2700 is the product of the first 5

triangular numbers.
2701 is the smallest number n which divides the average of the n

^{th} prime and the primes surrounding it.
2702 is the maximum number of regions space can be divided into by 21

spheres.
2704 is the number of necklaces with 9 white and 9 black beads.

2710 is an hexagonal prism number.

2712 is the number of

12-ominoes that tile the plane by translation.
2717 is the number of

9-hexes that do not tile the plane.
2718 is the

integer part of 1000e.
2719 is the largest odd number that can not be written in the form x

^{2} + y

^{2} + 10z

^{2}.

2722 has the property that if each digit is replaced by its

square, the resulting number is a square.
2725 is the number of fixed

octominoes.
2728 is a

Kaprekar number.
2729 has a

square with the first 3 digits the same as the next 3 digits.
2730 =

_{15}P_{3}.
2731 is a

Wagstaff prime.
2733 is the number of possible positions in Checkers after 5 moves.

2736 is an

octahedral number.
2737 is a strong

Friedman number.
2743 is a centered dodecahedral number.

2744 is the smallest number that can be written as the sum of a

cube and a 4^{th} power in more than one way.
2745 divides the sum of the

primes less than it.
2748 is ABC in

hexadecimal.
2749 is the smallest index of a

Fibonacci number whose first 9 digits are the digits 1-9 rearranged.
2751 is the number of ordered

partitions of 21 into distinct parts.
2752 is a structured snub cubic number.

2753 is the number of subsequences of {1,2,3,...13} in which every odd number has an even neighbor.

2757 is the number of possible configurations of pegs (up to symmetry) after 7 jumps in solitaire.

2758 has the property that placing the last digit first gives 1 more than triple it.

2766 in hexadecimal spells the word ACE.

2767 is the smallest number that can not be formed using the digit 1 at most 25 times, together with the symbols +, –, × and ÷.

2768 is

7-automorphic.
2769 is a value of n for which n and 5n together use each digit 1-9 exactly once.

2770 is the

Entringer number E(8,1).
2773 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with

integer dimensions less than 12.
2777 +

σ(2777) = 5555.
2780 = 1

^{8} + 2

^{7} + 3

^{6} + 4

^{5} + 5

^{4} + 6

^{3} + 7

^{2} + 8

^{1}.

2782 is the maximum value of n so
that there exist 4 denominations of stamps so that every postage from 1
to n can be paid for with at most 19 stamps.

2783 is the smallest number whose 9

^{th} power has 31 digits.

2786 is the 9

^{th} Pell-Lucas number.
2787 is a value of n for which the first n binary digits of

π form a prime.
2790 is the number of binary

partitions of 36.
2791 is a

Cuban prime.
2792 is the smallest number that can not be written using 13 copies of 13 and the operations +, –, ×, and ÷.

2793 is the number of inequivalent asymmetric

Ferrers graphs with 30 points.
2801 = 11111 in base 7.

2802 is the sum of its

proper divisors that contain the digit 4.
2805 is the smallest order of a

cyclotomic polynomial whose factorization contains 6 as a coefficient.
2806 is the number of

semigroups of order 6 with 2 idempotents.
2808 = (9 × 10 × 11 × 12 × 13) / (9 + 10 + 11 + 12 + 13) .

2810 has the property that the concatenation of its

prime factors in increasing order is a square.
2811 is the number of inequivalent

Ferrers graphs with 30 points.
2812 is the number of 8-pents.

2817 is a member of the

Fibonacci-type sequence starting with 1 and 4.
2821 is a

Carmichael number.
2824 is the smallest number whose

cube contains six 2's.
2828 is a value of n so that n(n+8) is a

palindrome.
2829 has a 4

^{th} power that is the sum of four 4

^{th} powers.

2832 is the number of ways to place 2 non-attacking

bishops on a 9×9 chessboard.
2834 is a

composite number n that divides the (n+1)^{st} Fibonacci number.
2835 is a

Rhonda number.
2842 is the smallest number with the property that its first 4 multiples contain the digit 8.

2844 is the sum of the first 15 numbers that have digit sum 15.

2846 is a value of n for which n

!!!! + 1 is prime.
2847 is a house number.

2848 is the smallest number whose

square contains 4 consecutive 1's.
2849 is the largest number n known whose base 11 representation is equal to

φ(n).
2850 is the

trinomial coefficient T(10,4).
2855 is the smallest number that can not be formed using the digit 1 at most 21 times, together with the symbols +, × and ^.

2856 = 17

!!!!!.
2857 is the number of

partitions of 44 in which no part occurs only once.
2858 has a

square with the first 3 digits the same as the next 3 digits.
2863 has a 10

^{th} root whose decimal part starts with the digits 1-9 in some order.

2867 has the property that the concatenation of its

prime factors in increasing order is a square.
2868 has a 4

^{th} power containing only 4 different digits.

2869 is a centered icosahedral number.

2870 is the sum of the first 20

squares.
2871 is a cubic star number.

2872 is the 15

^{th} Tetranacci number.
2874 is the number of

multigraphs with 5 vertices and 12 edges.
2876 is the number of 8-hepts.

2878 is the number of

integers with complexity 28.
2879 is the smallest number with

complexity 27.
2880 = 4! × 5!.

2881 has a base 3 representation that ends with its base 6 representation.

2882 has a base 3 representation that ends with its base 6 representation.

2888 is the first of five consecutive

squareful numbers.
2889 is a number n for which n

^{2}+1 is 5 times another square.

2890 is the smallest number in base 9 whose

square contains the same digits in the same proportion.
2893 is the number of

planar 2-connected graphs with 8 vertices.
2895 is the smallest n for which 38n contains only 0's and 1's.

2897 is a

Markov number.
2900 is the number of

self-avoiding walks in a quadrant of length 10.
2907 is the

trinomial coefficient T(9,1).
2910 is the number of

partitions of 48 into distinct parts.
2911 is a value of n for which

σ(n-1) = σ(n+1).
2913 is a value of n for which

σ(n-1) + σ(n+1) = σ(2n).
2914 is a value of n for which

σ(n-1) = σ(n+1).
2915 is a

Lucas-Carmichael number.
2916 is a

Friedman number.
2917 is the number of digits of the 21

^{st} Mersenne prime.
2918 is the number of ways to break {1,2,3, . . . ,15} into sets with equal sums.

2919 = (2 + 9 + 1 + 9) × (29 + 91 + 19).

2920 is a

heptagonal pyramidal number.
2922 is the sum of its

proper divisors that contain the digit 4.
2924 is an

amicable number.
2925 =

_{27}C_{3}.
2926 has a sum of digits equal to its largest

prime factor.
2928 is the number of

partitions of 45 in which no part occurs only once.
2931 is the number of

trees on 16 vertices with diameter 6.
2933 is a value of n for which

σ(φ(n)) = 2σ(n).
2937 is a value of n for which n and 5n together use each digit 1-9 exactly once.

2938 is the number of

binary rooted trees with 17 vertices.
2939 is a

right-truncatable prime.
2943 is the smallest value of n for which n and 6n together use each digit 1-9 exactly once.

2947 is the smallest number whose 5

^{th} power starts with 4 identical digits.

2950 is the maximum number of pieces a

torus can be cut into with 25 cuts.
2952 is the maximum number of regions a

cube can be cut into with 26 cuts.
2953 is the smallest number whose

cube contains six 7's.
2955 has a 5

^{th} power whose digits all occur twice.

2958 is the number of

multigraphs with 21 vertices and 4 edges.
2964 is a

Smith brother.
2965 is a

Smith brother.
2966 has the property that if each digit is replaced by its

square, the resulting number is a square.
2967 is a value of n for which 5n and 7n together use each digit exactly once.

2970 is a

harmonic divisor number.
2971 is the index of a

prime Fibonacci number.
2973 is a value of n for which n and 5n together use each digit 1-9 exactly once.

2974 is a value of n for which

σ(n) = σ(n+1).
2978 is the number of unlabeled

distributive lattices with 17 elements.
2981 is the closest

integer to e^{8}.
2982 is a value of n so that n(n+7) is a

palindrome.
2983 is the number of

trees on 28 vertices with diameter 4.
2984 is the number of different products of subsets of the set {1, 2, 3, ... 15}.

2988 is the number of

series-reduced trees with 20 vertices.
2989 in hexadecimal spells the word BAD.

2991 uses the same digits as

φ(2991).
2992 is the closest

integer to 19^{e}.
2993 is the number of digits of the 22

^{nd} Mersenne prime.
2996 is the number of terms in the 15

^{th} derivative of f(f(f(x))).

2997 = 222 + 999 + 999 + 777.

2998 is a value of n so that n(n+3) is a

palindrome.
2999 = 2 + 999 + 999 + 999.

3000 is the number of symmetric arrangements of 7 non-attacking

queens on a 7×7 chessboard.
3001 is 1/24 of the 24

^{th} Fibonacci number.
3003 is the only number known to appear 8 times in

Pascal's triangle.
3005 is the number of functions from {1,2,3,4,5} to itself that are not

injections.
3006 has a

square with the last 3 digits the same as the 3 digits before that.
3008 is the number of symmetric

plane partitions of 29.
3010 is the number of

partitions of 27.
3012 is the sum of its

proper divisors that contain the digit 5.
3015 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
3016 is a value of n for which n

φ(n) is a palindrome.
3020 is the closest

integer to π^{7}.
3024 =

_{9}P_{4}.
3025 is the sum of the first 10

cubes.
3026 is the number of 10-ominoes that tile the plane

isohedrally.
3028 are the first 4 digits of 5

^{3028}.

3031 is the number of

7-kings.
3032 is the number of

trees on 19 vertices with diameter 5.
3036 is the sum of its

proper divisors that contain the digit 5.
3038 has a

square that remains square when a 9 is appended to it.
3044 is the number of

nonisomorphic unlabeled binary relations on 4 elements.
3045 = 196 + 197 + . . . + 210 = 211 + 212 + . . . + 224.

3049 is the number of ways to tile a 8×4 rectangle with

integer-sided squares.
3053 in hexadecimal spells the word BED.

3054 = 6 × 7 × 8 × 9 + 6 + 7 + 8 + 9.

3055 is a number with the property that the

root-mean-square of its divisors is an integer.
3056 is a structured snub dodecahedral number.

3057 is the number of

rooted ternary trees with 12 vertices.
3058 is the number of 7-digit

triangular numbers.
3059 is a

centered cube number.
3060 =

_{18}C_{4}.
3063 is a

perfect totient number.
3066 is the average of the first 853

primes.
3068 is the number of

10-ominoes that tile the plane.
3069 is a

Kaprekar constant in base 2.
3070 is the number of paraffins with 9 carbon atoms.

3071 is a

Thabit number.
3072 is the smallest number with exactly 22

divisors.
3074 is the number of binary

partitions of 37.
3077 is the

rectilinear crossing number of complete graph K_{23}
3078 is a

pentagonal pyramidal number.
3080 is the number of drawings of the

complete graph K_{9} with a minimal number of Achilles number.
3089 is the smallest

prime so that it and the next 2 primes all end in 9.
3092 is a structured truncated tetrahedral number.

3094 = 21658 / 7, and each digit is contained in the equation exactly once.

3096 is the number of 3×3×3 sliding puzzle positions that require exactly 7 moves to solve.

3097 is the largest known number n
with the property that in every base, there exists a number that is n
times the sum of its digits.

3101 is the number of ways to color the vertices of a triangle with 21 colors, up to rotation.

3103 =

_{22}C_{3} + _{22}C_{1} + _{22}C_{0} + _{22}C_{3}.
3105 is a member of the

Fibonacci-type sequence starting with 2 and 7.
3106 is both the sum of the digits of the 16

^{th} and the 17

^{th} Mersenne prime.
3107 is the number of ways to divide a 10×10 grid of points into two sets using a straight line.

3109 is the smallest

prime n so that n/π(n) > 7.
3110 = 22222 in base 6.

3112 is the number of 10-digit strings where consecutive digits differ by exactly 1.

3114 has a

square containing only 2 digits.
3115 has the property that if each digit is replaced by its

square, the resulting number is a cube.
3119 is a

right-truncatable prime.
3120 is the product of the first 6

Fibonacci numbers.
3121 = 3121

_{5} + 3121

_{7} + 3121

_{8}.

3122 is the number of ordered sequences of coins totaling 29 cents.

3124 = 44444 in base 5.

3125 is a strong

Friedman number.
3126 is a

Sierpinski Number of the First Kind.
3127 is the product of two consecutive

primes.
3135 is the smallest order of a

cyclotomic polynomial whose factorization contains 7 as a coefficient.
3136 is a

square that remains square if all its digits are decremented.
3137 is the number of

planar partitions of 17.
3139 is the 9

^{th} central trinomial coefficient.
3141 is the

integer part of 1000 π.
3146 is a structured deltoidal hexacontahedral number.

3148 is the number of different

degree sequences possible for a graph with 9 vertices.
3150 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
3153 = 1

^{1} + 3

^{3} + 5

^{5}.

3156 is the sum of its

proper divisors that contain the digit 5.
3159 is the number of

trees with 14 vertices.
3160 is the largest known value of n for which

_{2n}C_{n} is not divisible by the first 5 primes.
3161 is the smallest number whose

square begins with three 9's.
3162 is the largest number whose

square has 6 digits.
3163 is the smallest number whose

square has 7 digits.
3168 has a

square whose reverse is also a square.
3169 is a

Cuban prime.
3171 is the sum of the

squares of 3 consecutive primes.
3173 is the number of different

degree sequences possible for a graph with 16 edges.
3174 is the first of four consecutive

squareful numbers.
3178 = 4321 in base 9.

3179 is the number of

13-ominoes that tile the plane by translation.
3180 has a base 3 representation that ends with its base 5 representation.

3181 has a base 3 representation that ends with its base 5 representation.

3182 has a base 3 representation that ends with its base 5 representation.

3184 is a value of n for which |cos(n)| is smaller than any previous

integer.
3185 is the number of ways to legally add 2 sets of parentheses to a product of 13 variables.

3186 is a value of n for which

_{2n}C_{n} is not divisible by 3, 5, or 7.
3187 is the smallest value of n for which n and 8n together use each digit 1-9 exactly once.

3189 is the number of

non-commutative non-associative closed binary operations.
3190 is a

narcissistic number in base 7.
3191 is the smallest number whose

reciprocal has period 29.
3192 is the number of

planar graphs with 8 vertices, all with degree 2 or more.
3195 is the number of congruency classes of triangles with vertices from a 12×12 grid of points.

3200 is the number of

graceful permutations of length 13.
3203 has the property that if each digit is replaced by its

square, the resulting number is a square.
3206 is the smallest number whose

square contains 8 different digits.
3210 is the smallest 4-digit number with decreasing digits.

3212 = 3

^{7} + 2

^{9} + 1

^{7} + 2

^{9}.

3214 is the maximum number of regions a circle can be cut into by joining 17 points on the circumference with straight lines.

3216 is the smallest number with the property that its first 6 multiples contain the digit 6.

3217 is the exponent of a

Mersenne prime.
3218 has the property that the concatenation of its

prime factors in increasing order is a square.
3225 is the number of

symmetric 3×3 matrices in base 5 with determinant 0.
3226 is the number of

12-iamonds without holes.
3229 is a value of n for which one more than the product of the first n

primes is prime.
3232 is the number of isomers of C

_{12}H

_{24} without any double bonds.

3237 is the number of

groupoids on 3 elements with no symmetry.
3240 is the number of 3×3×3

Rubik's cube positions that require exactly 3 moves to solve.
3242 has a

square with the first 3 digits the same as the next 3 digits.
3243 in hexadecimal spells the word CAB.

3244 is the number of asymmetric

trees with 18 vertices.
3245 in hexadecimal spells the word CAD.

3247 is the number of

connected graphs with 9 vertices and 25 edges.
3248 is the number of legal bishop moves in Chess.

3249 is the smallest

square that is comprised of two squares that overlap in one digit.
3250 is a value of n for which

_{2n}C_{n} is not divisible by 3, 5, or 7.
3251 is a number n for which n, n+2, n+6, and n+8 are all

prime.
3252 is the number of

graphs with 9 vertices and 11 edges.
3254 = 33 + 2222 + 555 + 444.

3255 is a value of n for which

φ(n) = φ(n+1).
3259 = 33 + 2222 + 5 + 999.

3262 is the number of

graphs with 9 vertices that have 6 automorphisms.
3264 is the number of

partitions of 49 into distinct parts.
3265 is the smallest n for which 34n contains only 0's and 1's.

3267 = 12345 in base 7.

3274 = 303022

_{4} = 101044

_{5}, each using 3 different digits exactly twice.

3276 =

_{28}C_{3}.
3277 is a

Poulet number.
3280 = 11111111 in base 3.

3281 is the sum of consecutive

squares in 2 ways.
3282 is the sum of its

proper divisors that contain the digit 4.
3283 is the number of 3×3 sliding puzzle positions that require exactly 15 moves to solve starting with the hole on a side.

3285 is the magic constant for a 9×9×9

magic cube.
3286 is the number of stable patterns with 16 cells in Conway's game of

Life.
3290 is an enneagonal pyramidal number.

3292 is the number of ways to tile a 4×27 rectangle with 4×1 rectangles.

3294 is a value of n for which 6n and 7n together use each digit exactly once.

3295 is the number of self-dual binary codes of length 32.

3296 is the number of lines passing through at least 2 points of an 11×11 grid of points.

3297 is a value of n for which 5n and 7n together use each digit exactly once.

3298 is the number of

trees with 7 vertices.
3300 is the number of

groupoids on 4 elements.
3301 is a value of n for which the n

^{th} Fibonacci number begins with the digits in n.
3302 is the maximum number of pieces a

torus can be cut into with 26 cuts.
3303 is a centered octahedral number.

3304 is the maximum number of regions a

cube can be cut into with 27 cuts.
3305 is the number of rectangles with corners on an 10×10 grid of points.

3306 is the number of

non-associative closed binary operations on a set with 3 elements.
3309 is the number of ways to break {1,2,3, . . . ,16} into sets with equal sums.

3311 is the sum of the first 21

squares.
3312 = 33

^{2} + 12

^{2}.

3313 is the smallest

prime number where every digit d occurs d times.
3318 has exactly the same digits in 3 different bases.

3320 has a base 4 representation that ends with 3320.

3321 has a base 4 representation that ends with 3321.

3322 has a base 4 representation that ends with 3322.

3323 has a base 4 representation that ends with 3323.

3324 is the maximum value of n so
that there exist 4 denominations of stamps so that every postage from 1
to n can be paid for with at most 20 stamps.

3325 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with

integer dimensions less than 13.
3326 is the smallest integer ratio of a 17-digit number to its product of digits.

3329 is a

Padovan number.
3330 is a value of n for which n-1 and n+1 are

twin primes, and so are 2n-1 and 2n+1.
3331 is the number of

monoids of order 7 with 3 idempotents.
3333 is a

repdigit.
3334 is the number of

12-iamonds.
3335 is the smallest number whose

square contains 4 consecutive 2's.
3337 has a

cube with only odd digits.
3338 is a member of the

Fibonacci-type sequence starting with 3 and 7.
3339 is a value of n for which

σ(n) = 3φ(n).
3340 = 3333 + 3 + 4 + 0.

3341 = 3333 + 3 + 4 + 1.

3342 = 3333 + 3 + 4 + 2.

3343 = 3333 + 3 + 4 + 3.

3344 = 3333 + 3 + 4 + 4.

3345 = 3333 + 3 + 4 + 5.

3346 = 3333 + 3 + 4 + 6.

3347 = 3333 + 3 + 4 + 7.

3348 = 3333 + 3 + 4 + 8.

3349 = 3333 + 3 + 4 + 9.

3358 is the sum of the

squares. of the first 11 primes.
3360 =

_{16}P_{3}.
3361 is the number of quasi-

triominoes that fit inside a 12×12 grid.
3362 has a

square whose digits each occur twice.
3363 is a number n for which n

^{2}+1 is double another square.

3366 = (1

^{9} + 2

^{9} + 3

^{9}) / (1 × 2 × 3).

3367 is the smallest number which can be written as the difference of 2

cubes in 3 ways.
3368 is the number of ways that 5 non-attacking

bishops can be placed on a 5×5 chessboard.
3369 is a

Kaprekar constant in base 4.
3375 is a

Friedman number.
3376 is the number of digits of the 23

^{rd} Mersenne prime.
3378 is a

Friedman number.
3379 is a number whose

square and cube use different digits.
3380 would be

prime if preceded and followed by a 1, 3, 7, or 9.
3381 is the number of ways to 14-color the faces of a

tetrahedron.
3382 is a value of n for which 2

φ(n) = φ(n+1).
3383 has the property that the sum of its

prime factors is equal to the product of its digits.
3386 has a

square whose digits each occur twice.
3390 is a value of n for which n-1 and n+1 are

twin primes, and so are 2n-1 and 2n+1.
3400 is a

truncated tetrahedral number.
3402 can be written as the sum of 2, 3, 4, or 5 positive

cubes.
3403 is a

triangular number that is the product of two primes.
3404 is the number of binary

partitions of 38.
3405 is a structured great rhombicosidodecahedral number.

3408 = 3

^{3} + 4

^{4} + 5

^{5}.

3410 is a truncated square pyramid number.

3411 is the number of inequivalent asymmetric

Ferrers graphs with 31 points.
3412 = 2

^{2} + 3

^{3} + 4

^{4} + 5

^{5}.

3413 = 1

^{1} + 2

^{2} + 3

^{3} + 4

^{4} + 5

^{5}.

3417 is a

hexagonal pyramidal number.
3420 is the order of a

non-cyclic simple group.
3427 is a member of the

Fibonacci-type sequence starting with 1 and 5.
3431 is the number of inequivalent

Ferrers graphs with 31 points.
3432 is the 7

^{th} central binomial coefficient.
3433 is a

narcissistic number in base 6.
3435 = 3

^{3} + 4

^{4} + 3

^{3} + 5

^{5}.

3439 is a

rhombic dodecahedral number.
3440 is the closest

integer to 20^{e}.
3444 is a

stella octangula number.
3447 is the smallest value of n for which 2n and 5n together use the digits 1-9 exactly once.

3451 is the number of

conjugacy classes of the alternating group A_{31}.
3456 has digits in

arithmetic sequence.
3457 is a

Proth prime.
3459 has a 6

^{th} root that starts 3.88888....

3461 is a number n for which n, n+2, n+6, and n+8 are all

prime.
3462 is the number of integer solutions to 1 = 1/x

_{1} + 1/x

_{2} + 1/x

_{3} + 1/x

_{4} + 1/x

_{5} + 1/x

_{6} for 1≤x

_{1}≤x

_{2}≤x

_{3}≤x

_{4}≤x

_{5}≤x

_{6}.

3465 = 15

!!!!.
3468 = 68

^{2} - 34

^{2}.

3476 is a value of n for which n

!! - 1 is prime.
3478 has the property that dropping its first and last digits gives its largest

prime factor.
3480 is a

Perrin number.
3482 is the smallest number n so that n

^{2} is 1 more than 43 times a

square.
3485 is the maximum value of n so
that there exist 8 denominations of stamps so that every postage from 1
to n can be paid for with at most 8 stamps.

3486 has a

square that is formed by 3 squares that overlap by 1 digit.
3487 is the number of squares in a 14×14 grid of squares with diagonals drawn.

3488 has a 5

^{th} root that starts 5.11111....

3489 is the smallest number whose

square has the first 3 digits the same as the last 3 digits.
3492 is the number of labeled

semigroups of order 4.
3498 is a number whose sum of

divisors is a 5^{th} power.
3499 in hexadecimal spells the word DAB.

3501 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
3502 is the number of 3×3×3

Rubik's cube positions that can result from 3 quarter or half turns.
3507 is a value of n for which n! - 1 is

prime.
3510 = 6666 in base 8.

3511 is the largest known

Wieferich prime.
3521 = 3333 + 55 + 22 + 111.

3522 is the sum of its

proper divisors that contain the digit 7.
3525 is a

Pentanacci number.
3527 is the number of ways to fold a strip of 10 stamps.

3528 is an

Achilles number.
3531 is a value of n for which

φ(n) = φ(n-2) - φ(n-1).
3534 is the number of 5-step self-avoiding walks on the cubic lattice.

3536 is a

heptagonal pyramidal number.
3539 is a value of n for which |cos(n)| is smaller than any previous

integer.
3541 is the smallest number whose

reciprocal has period 20.
3542 is the number of ways to write 16 as an ordered sum of positive

integers, where adjacent numbers are different.
3543 has a

cube containing only 3 different digits.
3552 is a value of n for which n

φ(n) is a palindrome.
3554 +

σ(3554) = 8888.
3563 is a house number.

3564 divides 1

^{1} + 2

^{2} + 3

^{3} +

^{ . . .} + 3564

^{3564}.

3570 is both a

triangular number and 6 times a triangular number.
3571 is the 17

^{th} Lucas number.
3575 is the smallest n for which 28n contains only 0's and 1's.

3577 is a

Kaprekar constant in base 2.
3579 has digits in

arithmetic sequence.
3581 is the smallest n for which 31n contains only 0's and 1's.

3583 is the smallest number requiring an

addition chain of length 16.
3584 is not the sum of 4 non-zero

squares.
3585 has a 10

^{th} power that contains the same digits as 9036

^{9}.

3588 is the maximum number of regions space can be divided into by 23

spheres.
3593 is a

prime that is the average of two 4^{th} powers.
3594 is the smallest number whose 9

^{th} power has 32 digits.

3596 is the number

permutations of {1,2,3,...,19} where adjacent numbers differ by no more than 2.
3599 is the product of

twin primes.
3600 is the order of a

perfect group.
3605 is a centered tetrahedral number.

3607 is a

prime factor of 123456789.
3609 is the number of

multigraphs with 22 vertices and 4 edges.
3610 is a value of n for which n! - 1 is

prime.
3612 is a

narcissistic number in base 7.
3613 is a

narcissistic number in base 7.
3616 = 1111 in base 15.

3620 is the

trinomial coefficient T(16,12).
3622 is the number of ways of placing 26 points on a 13×13 grid so that no 3 points are on a line.

3623 times the 3623

^{th} prime is a palindrome.
3624 is the first of five consecutive

squareful numbers.
3626 is a member of the

Fibonacci-type sequence starting with 1 and 9.
3628 is the number of ways to place 3 non-attacking queens on a 7×7 chessboard.

3630 appears inside its 4

^{th} power.

3632 is a value of n for which n

φ(n) is a palindrome.
3635 has a

square with the first 3 digits the same as the next 3 digits.
3638 is the number of ways to stack 26 pennies in contiguous rows so that each penny lies on the table or on two pennies.

3640 = 13

!!!.
3641 is an hexagonal prism number.

3645 is the maximum

determinant of a binary 12×12 matrix.
3648 is the number of subsets of {1,2,3,...,15} that have a sum divisible by 9.

3650 is the number of binary

cube-free words of length 19.
3652 is the number of fixed

7-hexes.
3654 =

_{29}C_{3}.
3655 is the sum of consecutive

squares in 2 ways.
3657 is a structured truncated octahedral number.

3658 is the number of

forests with 13 vertices.
3660 is the number of

connected graphs with 6 vertices and 6 edges.
3663 is a

palindrome in base 8 and in base 10.
3664 is the number of

graphs with 10 vertices and 9 edges.
3665 would be

prime if preceded and followed by a 1, 3, 7, or 9.
3671 is the number of

9-abolos.
3673 is the number of ways a 8×1 rectangle can be surrounded by 8×1 rectangles.

3678 has a

square comprised of the digits 1-8.
3679 is the number of ways to stack 17 pennies in a line so that each penny lies on the table or on two pennies.

3681 is the maximum number of pieces a

torus can be cut into with 27 cuts.
3683 is the maximum number of regions a

cube can be cut into with 28 cuts.
3684 is a

Keith number.
3685 is a strong

Friedman number.
3686 would be

prime if preceded and followed by a 1, 3, 7, or 9.
3690 is the number of

trees on 29 vertices with diameter 4.
3691 is a number n for which n

^{2}+1 is triple another square.

3696 is the number of ways to color the vertices of a square with 11 colors, up to rotation.

3697 is the smallest number in base 6 whose

square contains the same digits in the same proportion.
3698 has a

square comprised of the digits 0-7.
3699 is the

rectilinear crossing number of complete graph K_{24}
3700 is the sum of the

squares of 4 consecutive primes.
3702 = 3 + 33 + 333 + 3333.

3703 is the smallest number that can not be formed using the digit 1 at most 26 times, together with the symbols +, –, × and ÷.

3705 is the

generalized Catalan number C(16,4).
3709 is a value of n for which 2n and 7n together use the digits 1-9 exactly once.

3710 is a number whose sum of

divisors is a 5^{th} power.
3711 is the number of

multigraphs with 6 vertices and 10 edges.
3714 is the number of

graphs with 8 vertices and edge-connectivity 1.
3715 is a member of the

Fibonacci-type sequence starting with 3 and 8.
3718 is the number of

partitions of 28.
3720 = 225 + 226 + . . . + 240 = 241 + 242 + . . . + 255.

3721 is the number of

partitions of 46 in which no part occurs only once.
3723 has a 4

^{th} power that is the sum of four 4

^{th} powers.

3728 is the smallest number whose 7

^{th} power has 25 digits.

3729 is a value of n for which n and 5n together use each digit 1-9 exactly once.

3731 is a dodecagonal pyramidal number.

3733 is a

right-truncatable prime.
3734 is the number of binary

partitions of 39.
3739 is a

right-truncatable prime.
3740 is the sum of consecutive

squares in 2 ways.
3743 is the number of

polyaboloes with 9 half squares.
3745 has a

square with the last 3 digits the same as the 3 digits before that.
3747 is the smallest number whose 9

^{th} power contains exactly the same digits as another 9

^{th} power.

3750 is the first of four consecutive

squareful numbers.
3751 has the same digits as the 3751

^{st} prime.
3752 is a cubic star number.

3753 has a

cube that is the sum of 3 positive cubes.
3760 is a substring of any power of itself.

3761 is the first year of the modern Hebrew calendar.

3762 is the number of

bicentered trees with 15 vertices.
3763 is the largest n so that

**Q**(√n) has class number 6.
3765 is the number of

series-reduced planted trees with 18 vertices.
3767 is the smallest number with

complexity 28.
3771 is a value of n for which 4n and 7n together use each digit exactly once.

3773 is a structured great rhombicubeoctahedral number.

3777 is a

Pentanacci-like number starting from 1, 1, 1, 1, and 1.
3780 is a highly abundant number.

3784 has a factorization using the same digits as itself.

3786 = 3

^{4} + 7

^{4} + 8 + 6

^{4}.

3788 is the number of

9-hexes that tile the plane.
3789 divides the sum of the digits of 3789!.

3791 is the number of symmetric

plane partitions of 30.
3792 occurs in the middle of its

square.
3793 is a

right-truncatable prime.
3795 is the sum of the first 22

squares.
3797 is a

right-truncatable prime.
3798 is a value of n for which 2n and 9n together use the digits 1-9 exactly once.

3802 is the nearest integer to (5 + 1/5)

^{5}.

3803 is the largest

prime factor of 123456789.
3804 is a member of the

Fibonacci-type sequence starting with 2 and 5.
3807 and its successor are both divisible by 4

^{th} powers.

3808 is the

generalized Catalan number C(12,5).
3810 is the number of ways to place a non-attacking white and black pawn on a 9×9 chessboard.

3811 is the number of

polycubes containing 8 cubes, if mirror images are not counted as different.
3812 is the maximum value of n so
that there exist 4 denominations of stamps so that every postage from 1
to n can be paid for with at most 21 stamps.

3813 is the number of

partitions of 47 in which no part occurs only once.
3816 is a truncated cube number.

3822 is the number of triangles of any size contained in the triangle of side 24 on a triangular grid.

3824 is the number of lines through exactly 2 points of a 12×12 grid of points.

3825 is a

Kaprekar constant in base 2.
3827 is a

composite number n that divides the (n+1)^{st} Fibonacci number.
3829 is the sum of the first 16 numbers that have digit sum 16.

3832 is the number of fixed

6-kings.
3834 is the number of

weakly connected directed graphs with 4 vertices.
3836 is the maximum number of

inversions in a permutation of length 7.
3840 = 10

!!.
3841 is the number of interior intersections when all the diagonals of a

regular 20-gon are drawn.
3843 is a value of n for which 7n and 9n together use each digit exactly once.

3846 is the number of

Hamiltonian cycles of a 4×11 rectangle graph.
3849 has a

square with the first 3 digits the same as the next 3 digits.
3850 is a structured octagonal anti-diamond number.

3855 is an odd number for which a

regular polygon is constructible by straightedge and compass.
3857 is the number of 6-dimentional

partitions of 7.
3859 is a member of the

Fibonacci-type sequence starting with 2 and 9.
3861 is the smallest number whose 4

^{th} power starts with 5 identical digits.

3864 is a strong

Friedman number.
3865 is a

Smith brother.
3871 is the sum of the

cubes of 3 consecutive primes.
3872 is an

Achilles number.
3873 is a

Kaprekar constant in base 4.
3876 =

_{19}C_{4}.
3882 is the sum of its

proper divisors that contain the digit 4.
3883 is the smallest number whose

cube contains 4 consecutive 6's.
3884 has a 5

^{th} root that starts 5.22222....

3888 is an

Achilles number.
3889 +

φ(3889) = 7777.
3893 is the number of

3-regular connected planar graphs with 18 vertices.
3894 is an

octahedral number.
3895 is the number of intersections when all the diagonals of a

regular 19-gon are drawn.
3896 is the number of ways to place 3 non-attacking

bishops on a 6×6 chessboard.
3897 divides the sum of the digits of 3897!.

3900 has a base 2 representation that is two copies of its base 5 representation concatenated.

3901 has a base 2 representation that ends with its base 5 representation.

3903 is a

Lucas 7-step number.
3906 = 111111 in base 5.

3907 = 15628 / 4, and each digit is contained in the equation exactly once.

3910 is the number of 3×3 sliding puzzle positions that require exactly 28 moves to solve starting with the hole in a corner.

3911 and its reverse are

prime, even if we append or prepend a 3 or 9.
3912 is a value of n for which 5n and 7n together use each digit exactly once.

3913 is a

Huay rhombic dodecahedral number.
3916 is a

triangular number whose internal digits are triangular and whose external digits are triangular.
3920 = (5+3) × (5+9) × (5+2) × (5+0).

3923 is a factor of 3924392539263927.

3925 is a

centered cube number.
3926 is the 12

^{th} open meandric number.
3927 has an 8

^{th} root whose decimal part starts with the digits 1-9 in some order.

3928 is the closest

integer to 21^{e}.
3929 is the number of

integers with complexity 29.
3937 is a

Kaprekar constant in base 2.
3938 is the number of 4×4 sliding puzzle positions that require exactly 11 moves to solve starting with the hole in a corner.

3939 is a structured truncated tetrahedral number.

3942 is a value of n for which n and 4n together use each digit 1-9 exactly once.

3952 has a sum of digits equal to its largest

prime factor.
3956 is the number of

conjugacy classes in the automorphism group of the 15 dimensional hypercube.
3957 is the number of ways to stack 32 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

3960 is a highly abundant number.

3967 is the smallest number whose 12

^{th} power contains exactly the same digits as another 12

^{th} power.

3968 and its successor are both divisible by 4

^{th} powers.

3969 is a

Kaprekar constant in base 2.
3972 is a strong

Friedman number.
3973 has a 4

^{th} power that is the sum of four 4

^{th} powers.

3977 has the property that dropping its first and last digits gives its largest

prime factor.
3978 is the number of ways to place 30 points on a 15×15 grid so that

no 3 points are on a line.
3979 is the number of

centered trees with 15 vertices.
3980 is the smallest multiple of 20 whose digits add to 20.

3982 is the smallest number whose 5

^{th} power has 18 digits.

3983 has the property that the concatenation of its

prime factors in increasing order is a square.
3984 is a

Heptanacci number.
3985 = 3333 + 9 + 88 + 555.

3986 has an 8

^{th} root that starts 2.81881881....

3987 is the closest

integer to 14^{π}.
3991 is the number of labeled graded

partially ordered sets with 5 elements.
3993 is a structured snub cubic number.

3994 is the number of

transitive relations on 4 labeled nodes.
3996 = (6

^{6} + 6

^{7} + 6

^{8} + 6

^{9}) / (6 × 7 × 8 × 9).

3999 is the smallest number whose digits add to 30.

4000 has a

cube that contains only even digits.
4002 has a

square with the first 3 digits the same as the next 3 digits.
4004 = (10 × 11 × 12 × 13 × 14) / (10 + 11 + 12 + 13 + 14) .

4005 is a

triangular number whose internal digits are triangular and whose external digits are triangular.
4006 =

_{14}C_{4} + _{14}C_{0} + _{14}C_{0} + _{14}C_{6}.
4008 has a

square with the last 3 digits the same as the 3 digits before that.
4010 is the magic constant of a 20×20 magic square.

4011 is the sum of the

squares of 3 consecutive primes.
4013 is a

prime factor of 1111111111111111111111111111111111.
4019 is a

prime that remains prime if any digit is deleted.
4023 is the number of ways to tile a 3×23 rectangle with 3×1 rectangles.

4029 is the number of regions formed when all diagonals are drawn in a

regular 19-gon.
4030 is a

weird number.
4031 is the sum of the

cubes of the first 6 primes.
4032 is the number of

connected bipartite graphs with 10 vertices.
4033 is a

Poulet number.
4037 is a member of the

Fibonacci-type sequence starting with 1 and 6.
4040 is an enneagonal pyramidal number.

4047 is a

hexagonal pyramidal number.
4048 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
4050 has the property that dropping its first and last digits gives its largest

prime factor.
4051 is the number of

partitions of 6 items into ordered lists.
4052 is the closest integer to sinh(9).

4053 has a

cube that contains only digits 5 and larger.
4055 is the smallest number whose

cube contains six 6's.
4056 is the number of possible rook moves on a 13×13 chessboard.

4059 is the sum of 3 consecutive

cubes.
4060 =

_{30}C_{3}.
4062 is the smallest number with the property that its first 8 multiples contain the digit 2.

4063 is a

Tribonacci-like number starting from 1, 1, and 1.
4064 is a value of n for which

σ(n) = σ(reverse(n)).
4068 is the number of ways to write 26 as the ordered sum of positive squares.

4071 is the number of ways to color the vertices of a triangle with 23 colors, up to rotation.

4074 is a value of n for which

σ(n) = 2reverse(n).
4077 has a

square whose digits each occur twice.
4078 is a value of n for which n

!!!! + 1 is prime.
4080 =

_{17}P_{3}.
4083 is the number of ways 12 people can line up so that only one person has a taller person in front of him.

4086 is a permutation of the sum of its

proper divisors.
4087 is the product of two consecutive

primes.
4088 is the maximum number of pieces a

torus can be cut into with 28 cuts.
4089 is a centered octahedral number.

4090 is the maximum number of regions a

cube can be cut into with 29 cuts.
4093 = 28651 / 7, and each digit is contained in the equation exactly once.

4094 is the

Entringer number E(8,2).
4095 and its reverse are both differences of positive 4

^{th} powers.

4096 is the smallest number with 13

divisors.
4097 is the smallest number (besides 2) that can be written as the sum of two

cubes or the sum of two 4^{th} powers.
4098 is the number of subsets of the 26

^{th} roots of unity that add to 1.
4099 has a

square with the last 3 digits the same as the 3 digits before that.
4100 = 5555 in base 9.

4104 can be written as the sum of 2

cubes in 2 ways.
4106 is a

Friedman number.
4112 is the number of necklaces possible with 17 beads, each being one of 2 colors.

4116 is the number of necklaces (that can't be turned over) possible with 16 beads, each being one of 2 colors.

4119 times the 4119

^{th} prime is a palindrome.
4120 has a

cube with a digit sum larger than its 7^{th} power.
4121 is a number whose product of digits is equal to its sum of digits.

4122 is the number of labeled

monoids of order 5 with fixed identity.
4124 is the number of binary

partitions of 40.
4128 is the smallest number with the property that its first 10 multiples contain the digit 2.

4132 is the number of

connected 3-regular bipartite graphs with 22 vertices.
4140 is the 8

^{th} Bell number.
4141 = 4141

_{5} + 4141

_{7} + 4141

_{8}.

4147 is a value of n for which

φ(n) = φ(reverse(n)).
4149 is a value of n for which

σ(n-1) = σ(n+1).
4150 = 4

^{5} + 1

^{5} + 5

^{5} + 0

^{5}.

4151 = 4

^{5} + 1

^{5} + 5

^{5} + 1

^{5}.

4152 = 4

^{5} + 1

^{5} + 5

^{5} + 2.

4153 = 4

^{5} + 1

^{5} + 5

^{5} + 3.

4154 = 4

^{5} + 1

^{5} + 5

^{5} + 4.

4155 = 4

^{5} + 1

^{5} + 5

^{5} + 5.

4156 = 4

^{5} + 1

^{5} + 5

^{5} + 6.

4157 = 4

^{5} + 1

^{5} + 5

^{5} + 7.

4158 = 4

^{5} + 1

^{5} + 5

^{5} + 8.

4159 = 4

^{5} + 1

^{5} + 5

^{5} + 9.

4160 = 4

^{3} + 16

^{3} + 0

^{3}.

4161 = 4

^{3} + 16

^{3} + 1

^{3}.

4163 is the number of inequivalent asymmetric

Ferrers graphs with 32 points.
4167 is a

Friedman number.
4175 has a

square comprised of the digits 0-7.
4176 has an 8

^{th} root whose decimal part starts with the digits 1-9 in some order.

4180 is the sum of the first 17

Fibonacci numbers.
4181 is the first

composite number in the Fibonacci sequence with a prime index.
4183 is a

narcissistic number in base 7.
4185 is the smaller number in a

Ruth-Aaron pair.
4186 is a

hexagonal, 13-gonal, triangular number.
4187 is the smallest

Rabin-Miller pseudoprime with an odd reciprocal period.
4188 is a value of n for which

σ(n-1) = σ(n+1).
4191 is the number of

graphs with 12 vertices and 10 edges.
4192 is the larger number in a

Ruth-Aaron pair.
4193 is the number of 3×3 sliding puzzle positions that require exactly 16 moves to solve starting with the hole on a side.

4195 has a sum of

prime factors that is equal to the sum of the prime factors of the two preceding numbers.
4196 is the number of

3-regular bipartite graphs with 22 vertices.
4199 is the product of 3 consecutive

primes.
4200 is divisible by its reverse.

4202 = 4202

_{5} + 4202

_{7} + 4202

_{8}.

4204 and the two numbers before it and after it are all products of exactly 3

primes.
4205 has the property that if each digit is replaced by its

square, the resulting number is a square.
4207 is the number of

cubic graphs with 16 vertices.
4209 is the number of

conjugacy classes of the alternating group A_{32}.
4210 is the number of

graphs with 10 vertices with clique number 7.
4211 is a number whose product of digits is equal to its sum of digits.

4215 is a centered dodecahedral number.

4216 is an octagonal pyramidal number.

4217 is the smallest number whose 8

^{th} power has 29 digits.

4219 is a

Cuban prime.
4220 is a number n for which the sum of the first n

composite numbers is a palindrome.
4222 is the number of

13-hexes with bilateral symmetry.
4223 is the maximum number of 12

^{th} powers needed to sum to any number.

4224 is a

palindrome that is one less than a square.
4225 is the smallest number that can be written as the sum of two

squares in 12 ways.
4231 is the number of labeled

partially ordered sets with 5 elements.
4232 is the number of different products of subsets of the set {1, 2, 3, ... 16}.

4233 is a

heptagonal pyramidal number.
4235 has a

cube that contains only digits 5 and larger.
4236 has a 4

^{th} power that is the sum of four 4

^{th} powers.

4237 is the number of ordered sequences of coins totaling 30 cents.

4240 is a

Leyland number.
4243 = 444 + 22 + 444 + 3333.

4244 is the total number of digits in all the 4-digit primes.

4249 is a value of n for which |cos(n)| is smaller than any previous

integer.
4252 is the smallest number in base 8 to have 5 different digits.

4253 is the exponent of a

Mersenne prime.
4254 is the number of

7-drafters.
4255 is a centered tetrahedral number.

4257 is the number of triangles formed by connecting the diagonals of a regular 11-gon.

4258 is the sum of the digits of the 18

^{th} Mersenne prime.
4260 is a value of n for which n+1, 2n+1, 3n+1, and 4n+1 are all

prime.
4264 is a number whose sum of

squares of the divisors is a square.
4267 has a 4

^{th} power that is the sum of four 4

^{th} powers.

4269 has a

cube whose first few digits are 77799797....
4276 is the number of (not necessarily distinct) sets of

Egyptian fractions that sum to 1 with smallest fraction 1/26.
4278 does not occur in its

factorial in base 2.
4279 is the smallest

semiprime super Catalan number.
4280 has a

square root whose decimal part starts with the digits 0-9 in some order.
4283 is the smallest number with

complexity 29.
4285 is a structured hexagonal diamond number.

4288 is a value of n for which n

!!!! + 1 is prime.
4290 is a value of n for which

_{2n}C_{n} is divisible by n^{2}.
4291 is the number of necklaces possible with 6 beads, each being one of 6 colors.

4293 has exactly the same digits in 3 different bases.

4294 is a value of n for which

σ(n) = φ(n) + φ(n-1) + φ(n-2).
4297 is the smallest

prime that is followed by 29 composite numbers.
4300 has the property that if each digit is replaced by its

square, the resulting number is a square.
4303 is the number of triangles of any size contained in the triangle of side 25 on a triangular grid.

4305 has exactly the same digits in 3 different bases.

4310 has exactly the same digits in 3 different bases.

4311 is the largest number n known with the property that n-2

^{k} is a

pseudoprime for all k>0.
4312 is the smallest number whose 10

^{th} power starts with 7 identical digits.

4320 = (6+4) × (6+3) × (6+2) × (6+0).

4321 has digits in

arithmetic sequence.
4324 is the sum of the first 23

squares.
4325 is a member of the

Fibonacci-type sequence starting with 4 and 9.
4329 is the only number n so that n, 2n, 4n, and 6n together contain every digit 1-9 exactly twice.

4330 is the number of

4-regular multigraphs with 10 vertices.
4332 = 444 + 3333 + 333 + 222.

4333 has a 4

^{th} power that is the sum of four 4

^{th} powers.

4335 = 444 + 3333 + 3 + 555.

4336 = 4 + 3333 + 333 + 666.

4337 is a value of n for which

φ(n) = φ(n-1) + φ(n-2).
4339 = 4 + 3333 + 3 + 999.

4340 is the number of 3×3 sliding puzzle positions that require exactly 27 moves to solve starting with the hole in the center.

4342 appears inside its 4

^{th} power.

4343 has the property that the sum of its

prime factors is equal to the product of its digits.
4347 is a value of n for which 2n and 5n together use the digits 1-9 exactly once.

4348 is the number of ways of placing 24 points on a 12×12 grid so that no 3 points are on a line.

4352 has a

cube that contains only even digits.
4355 = 2

^{4} + 3

^{5} + 4

^{6}.

4356 is two thirds of its reverse.

4357 is the smallest number with the property that its first 5 multiples contain the digit 7.

4359 is a

perfect totient number.
4361 is the number of different

degree sequences for graphs with 9 vertices.
4364 is a value of n for which

σ(n) = σ(n+1).
4365 is a value of n for which 4n and 9n together use each digit exactly once.

4368 =

_{16}C_{5}.
4369 is an odd number for which a

regular polygon is constructible by straightedge and compass.
4371 is a

Poulet number.
4374 and its successor are both divisible by 4

^{th} powers.

4375 is a

perfect totient number.
4376 and its reverse are both differences of positive

cubes.
4378 is the number of

partitions of 38 that do not contain 1 as a part.
4380 is the number of ways to place 2 non-attacking

bishops on a 10×10 chessboard.
4381 is a

stella octangula number.
4382 is the number of primitive sorting networks on 9 elements.

4388 divides 1

^{1} + 2

^{2} + 3

^{3} +

^{ . . .} + 4388

^{4388}.

4390 is a house number.

4392 is a value of n for which n and 4n together use each digit 1-9 exactly once.

4394 is a truncated square pyramid number.

4396 = 157 × 28 and each digit is contained in the equation exactly once.

4398 is the number of subsets of {1, 2, 3, ... 18} that do not contain solutions to x + y = z.

4402 has the property that if each digit is replaced by its

square, the resulting number is a square.
4406 is the number of

divisors of the 16^{th} perfect number.
4408 is the number of

20-iamonds with bilateral symmetry.
4410 is a

Padovan number.
4413 is the index of a

prime Euclid number.
4418 is the number of 7-nons.

4421 = 7! - 6! + 5! - 4 ! + 3! - 2! + 1!.

4422 is the maximum value of n so
that there exist 5 denominations of stamps so that every postage from 1
to n can be paid for with at most 15 stamps.

4423 is the exponent of a

Mersenne prime.
4424 2

^{5} + 3

^{5} + 4

^{5} + 5

^{5}.

4425 is the sum of the first five 5

^{th} powers.

4430 is the

rectilinear crossing number of complete graph K_{25}
4431 is the number of

graphs with 8 vertices that have 2 automorphisms.
4434 is the sum of its

proper divisors that contain the digit 7.
4435 uses the same digits as

φ(4435).
4436 is the number of ways to place 4 non-attacking

knights on a 5×5 chessboard.
4438 is the number of

15-hexes with reflectional symmetry.
4441 is the number of different solutions to ±1±2...±18 = 1.

4442 is a value of n for which

σ(n) is a repdigit.
4443 is a number n for which n

^{2}+1 is 10 times another square.

4444 is a

repdigit.
4445 is the smallest number that can be written as the sum of 4 distinct positive

cubes in 4 ways.
4447 is a

Cuban prime.
4449 has a 4

^{th} power that is the sum of four 4

^{th} powers.

4455 is the number of

permutations of 12 items that fix 8 elements.
4457 is the closest

integer to 22^{e}.
4460 is the number of 10-ominoes without holes.

4461 is the number of asymmetrical 10-ominoes.

4465 +

φ(4465) = 7777.
4467 is the number of terms in the 16

^{th} derivative of f(f(f(x))).

4473 is a value of n for which

σ(n) = 2reverse(n).
4475 = 6

^{2} + 7

^{3} + 8

^{4}.

4478 is the number of

fullerenes with 66 carbon atoms.
4480 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
4481 is a

prime that is the average of two 4^{th} powers.
4485 is the number of 3×3 sliding puzzle positions that require exactly 16 moves to solve starting with the hole in a corner.

4488 = 256 + 257 + . . . + 272 = 273 + 274 + . . . + 288.

4489 is a

square whose digits are non-decreasing.
4493 is the number of ways to divide a 11×11 grid of points into two sets using a straight line.

4495 =

_{31}C_{3}.
4498 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
4500 is the number of regions formed when all diagonals are drawn in a

regular 20-gon.
4502 is the number of unit

interval graphs with 10 vertices.
4503 is the largest number that is not the sum of 4 or fewer

squares of composites.
4505 is a

Zeisel number.
4506 is the sum of its

proper divisors that contain the digit 5.
4510 = 4444 + 55 + 11 + 0.

4511 = 4444 + 55 + 11 + 1.

4512 = 4444 + 55 + 11 + 2.

4513 = 4444 + 55 + 11 + 3.

4514 = 4444 + 55 + 11 + 4.

4515 = 4444 + 55 + 11 + 5.

4516 = 4444 + 55 + 11 + 6.

4517 = 4444 + 55 + 11 + 7.

4518 = 4444 + 55 + 11 + 8.

4519 = 4444 + 55 + 11 + 9.

4520 is the number of regions the

complex plane is cut into by drawing lines between all pairs of 20^{th} roots of unity.
4522 is the number of non-intersecting rook paths joining opposite corners of a 8×3 chessboard.

4523 has a

square in base 2 that is palindromic.
4524 is the maximum number of pieces a

torus can be cut into with 29 cuts.
4526 is the maximum number of regions a

cube can be cut into with 30 cuts.
4527 is a value of n for which n and 7n together use each digit 1-9 exactly once.

4530 has the property that the sum of the

factorials of its digits is its largest prime factor.
4535 is the number of unlabeled

topologies with 7 elements.
4536 is the

Stirling number of the first kind s(9,6).
4541 has a

square with the first 3 digits the same as the next 3 digits.
4542 is the number of

trees on 20 vertices with diameter 5.
4544 is a

Kaprekar number for cubes.
4547 is a value of n for which one more than the product of the first n

primes is prime.
4548 is the sum of its

proper divisors that contain the digit 7.
4550 is the

Stirling number of the second kind S(15,13).
4552 has a

square with the first 3 digits the same as the next 3 digits.
4556 is the

trinomial coefficient T(17,13).
4558 is a member of the

Fibonacci-type sequence starting with 1 and 4.
4562 is the number of

divisors of the 17^{th} perfect number.
4563 is an

Achilles number.
4565 is the number of

partitions of 29.
4567 has digits in

arithmetic sequence.
4576 is a

truncated tetrahedral number.
4579 is an

octahedral number.
4582 is the number of

partitions of 52 into distinct parts.
4583 is a value of n for which one less than the product of the first n

primes is prime.
4589 is the index of a

Fibonacci number whose first 9 digits are the digits 1-9 rearranged.
4591 is a value of n for which n and 8n together use each digit 1-9 exactly once.

4600 is a decagonal pyramidal number.

4604 is a value of n for which |cos(n)| is smaller than any previous

integer.
4607 is a

Woodall number.
4608 is the number of ways to place 2 non-attacking kings on a 10×10 chessboard.

4609 is a

Cullen number.
4610 is a

Perrin number.
4613 is the number of

graphs with 10 edges.
4614 is the number of ways to stack 27 pennies in contiguous rows so that each penny lies on the table or on two pennies.

4615 is a value of n for which

σ(φ(n)) = 2σ(n).
4616 has a

square comprised of the digits 0-7.
4619 is a value of n for which 4n and 5n together use each digit exactly once.

4620 is the largest order of a

permutation of 30 or 31 elements.
4621 =

π(4×6×2×1×(4+6+2+1)).
4622 is the number of

12-ominoes that contain 1 hole.
4623 is a value of n for which

σ(n) = 2reverse(n).
4624 = 4

^{4} + 4

^{6} + 4

^{2} + 4

^{4}.

4625 is the number of

trees on 16 vertices with diameter 7.
4628 is a

Friedman number.
4631 has a

cube with only odd digits.
4640 is the number of different

score sequences of an 11-team round robin tournament.
4641 is a

rhombic dodecahedral number.
4642 is the smallest number whose

cube has 11 digits.
4644 is a value of n for which 7n and 9n together use each digit exactly once.

4645 has the property that the concatenation of its

prime factors in increasing order is a square.
4647 is a member of the

Fibonacci-type sequence starting with 1 and 7.
4649 has a 9

^{th} root that starts 2.55555....

4650 is the maximum number of regions space can be divided into by 25

spheres.
4652 is the number of labeled

connected graphs with 6 vertices that have chromatic number 4.
4653 is a value of n for which n and 6n together use each digit 1-9 exactly once.

4655 is the number of

10-ominoes.
4657 is a number that does not have any digits in common with its

cube.
4662 is the number of ways to place 2 non-attacking

knights on a 10×10 chessboard.
4663 is the number of

12-ominoes that contain holes.
4665 = 33333 in base 6.

4666 is the number of tilted rectangles with vertices in a 13×13 grid.

4672 is a permutation of the sum of its

proper divisors.
4675 2

^{4} + 3

^{4} + 4

^{4} + 5

^{4} + 6

^{4} + 7

^{4}.

4676 is the sum of the first seven 4

^{th} powers.

4680 is a value of n for which n, n

^{2}, and n

^{3} have the same digit sum.

4681 = 11111 in base 8.

4682 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 14.

4683 is the number of orderings of 6 objects with ties allowed.

4684 is the number of subsets of {1,2,3,...,15} that have a sum divisible by 7.

4685 is the number of

anisohedral 15-hexes.
4686 is the denominator of the 70

^{th} Bernoulli number.
4687 is a value of n for which

σ(φ(n)) = 3σ(n).
4688 is

2-automorphic.
4689 is a value of n for which n and 8n together use each digit 1-9 exactly once.

4691 is a value of n for which n and 8n together use each digit 1-9 exactly once.

4695 are the first 4 digits of 4

^{4695}.

4697 is a value of n for which

φ(n) = φ(reverse(n)).
4698 is the smallest number so that it and its reverse are divisible by 54.

4705 is the sum of consecutive

squares in 2 ways.
4709 is the number of symmetric

plane partitions of 31.
4713 is a value of n such that the n

^{th} Cullen number is prime.
4714 is the smallest number whose

square begins with four 2's.
4720 is a structured truncated cubic number.

4722 is the number of lines passing through at least 2 points of an 12×12 grid of points.

4723 is the index of a

prime Fibonacci number.
4725 is an odd

abundant number.
4726 is the smallest number whose

cube contains 5 consecutive 5's.
4727 is the sum of the

squares. of the first 12 primes.
4730 is the number of

multigraphs with 5 vertices and 13 edges.
4732 is a number that does not have any digits in common with its

cube.
4734 is the sum of its

proper divisors that contain the digit 7.
4735 is a value of n for which 4n and 5n together use each digit exactly once.

4738 is a

Menage number.
4740 is the

trinomial coefficient T(10,3).
4741 is a value of n for which 4n and 5n together use each digit exactly once.

4743 is a value of n for which 2n and 5n together use the digits 1-9 exactly once.

4748 is a value of n for which

σ(n) = φ(n) + φ(n-1) + φ(n-2).
4750 is a

hexagonal pyramidal number.
4751 is the starting location of 8888 in the decimal expansion of

π.
4752 = (4+4) × (4+7) × (4+5) × (4+2).

4755 has a

cube whose digits occur with the same frequency.
4757 is the number of ordered

partitions of 23 into distinct parts.
4758 does not occur in its

factorial in base 2.
4760 is the sum of consecutive

squares in 2 ways.
4761 is the number of subsets of {1,2,3,...,15} that have an

integer average.
4762 is the smallest number not a power of 10 whose

square contains the same digits.
4764 is an hexagonal prism number.

4766 is the number of

rooted trees with 12 vertices.
4769 is a value of n for which 4n and 5n together use each digit exactly once.

4776 is a structured pentagonal hexacontahedral number.

4780 has a

square whose digits each occur twice.
4781 is the number of (not necessarily distinct) sets of

Egyptian fractions that sum to 1 with smallest fraction 1/20.
4784 has a sum of digits equal to its largest

prime factor.
4785 has a

square that is the sum of a cube and a 4^{th} power.
4787 is a value of n for which one more than the product of the first n

primes is prime.
4788 is a

Keith number.
4793 = 4444 + 7 + 9 + 333.

4797 is a cubic star number.

4798 is a value of n for which n

!!! + 1 is prime.
4801 is a number n for which n

^{2}+1 is 6 times another square.

4802 can be written as the sum of 2 or 3 positive 4

^{th} powers.

4804 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
4807 is the smallest quasi-Carmichael number in base 10.

4815 is the number of ways to stack 33 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

4819 is a

Tetranacci-like number starting from 1, 1, 1, and 1.
4823 is the number of triangles of any size contained in the triangle of side 26 on a triangular grid.

4831 is the smallest

prime so that it and the next 2 primes all end in 1.
4832 is a number whose

square contains the same digits.
4835 is the number of

anisohedral 14-hexes.
4843 is a value of n for which

σ(φ(n)) = 2σ(n).
4845 =

_{20}C_{4}.
4848 is the number of

quaternary square-free words of length 8.
4850 is a

Wedderburn-Etherington number.
4851 is a

pentagonal pyramidal number.
4852 is the sum of the

squares of 4 consecutive primes.
4854 does not occur in its

factorial in base 2.
4860 is the order of a

perfect group.
4862 is the 9

^{th} Catalan number.
4863 is the smallest number that cannot be written as the sum of 273 8

^{th} powers.

4866 is the number of

partitions of 48 in which no part occurs only once.
4869 is a value of n for which 3n and 8n together use each digit exactly once.

4875 is the number of

graphs with 10 vertices and 3 cycles.
4876 divides the sum of the first 681

composite numbers.
4877 is the largest

prime factor of 87654321.
4878 is the number of

alternating knots with 13 crossings.
4879 = 238 + 0 + 4641 and has the

square 23804641.
4889 2

^{6} + 3

^{6} + 4

^{6}.

4890 is a

narcissistic number in base 5.
4891 is a

narcissistic number in base 5.
4893 is a value of n for which 2n and 7n together use the digits 1-9 exactly once.

4895 is the product of two consecutive

Fibonacci numbers.
4896 =

_{18}P_{3}.
4899 is the sum of the

squares of 3 consecutive primes.
4900 is the only non-trivial number which is both

square and square pyramidal.
4901 has a base 3 representation that begins with its base 7 representation.

4902 is the starting location of 2222 in the decimal expansion of

π.
4905 is the sum of all the 2-digit numbers.

4911 has a 9

^{th} power whose first few digits are 16616111....

4913 is the

cube of the sum of its digits.
4917 is the

trinomial coefficient T(11,5).
4919 is a

prime that remains prime if any digit is deleted.
4920 = 6666 in base 9.

4922 is a number whose sum of

divisors is a 5^{th} power.
4923 and the two numbers before it and after it are all products of exactly 3

primes.
4924 and the two numbers before it and after it are all products of exactly 3

primes.
4927 is a value of n for which 4n and 5n together use each digit exactly once.

4928 is a structured truncated tetrahedral number.

4930 = 6677

_{9} = 2A2A

_{12} = 2323

_{13} = 1010

_{17}, each using two digits exactly twice each.

4931 is a value of n for which 2n and 7n together use the digits 1-9 exactly once.

4933 is the number of digits in the 14

^{th} Fermat number.
4936 = 4 + 44 + 444 + 4444.

4939 has the property that the concatenation of its

prime factors in increasing order is a square.
4941 is a

centered cube number.
4944 is a value of n for which n

φ(n) is a palindrome.
4949 has a 4

^{th} power that is the sum of four 4

^{th} powers.

4950 is both a

triangular number and 5 times a triangular number.
4952 is the closest

integer to 15^{π}.
4959 is a value of n for which |cos(n)| is smaller than any previous

integer.
4960 =

_{32}C_{3}.
4961 is a

Hexanacci-like number starting from 1, 1, 1, 1, 1, and 1.
4964 is the number of binary

partitions of 42.
4967 is the number of

partitions of 49 in which no part occurs only once.
4974 is the sum of its

proper divisors that contain the digit 8.
4975 is a value of n for which n

!!! + 1 is prime.
4979 is a centered tetrahedral number.

4980 has the same digits as the 4980

^{th} prime.
4982 is a number whose sum of

divisors is a 5^{th} power.
4985 is the number of

graphs with 8 vertices with clique number 4.
4988 is the smallest multiple of 29 whose digits add to 29.

4990 is the maximum number of pieces a

torus can be cut into with 30 cuts.
4991 is a

Lucas-Carmichael number.
4992 is the maximum number of regions a

cube can be cut into with 31 cuts.
4993 is a

Proth prime.
4995 has a 5

^{th} power that is closer to a

cube than a square.
4999 is the smallest number whose digits add to 31.

5000 is the largest number whose English name does not repeat any letters.

5001 appears inside its 4

^{th} power.

5002 has a 4

^{th} power containing only 4 different digits.

5005 is the smallest

palindromic product of 4 consecutive primes.
5009 would be

prime if preceded and followed by a 1, 3, 7, or 9.
5010 has a

square with the last 3 digits the same as the 3 digits before that.
5016 is a

heptagonal pyramidal number.
5020 is an

amicable number.
5024 is a member of the

Fibonacci-type sequence starting with 2 and 7.
5026 is the number of

connected graphs with 11 vertices and 1 cycle.
5030 is the closest

integer to 23^{e}.
5036 and the two numbers before it and after it are all products of exactly 3

primes.
5039 is the number of

planar partitions of 18.
5040 = 7!

5041 is the largest

square known of the form n! + 1.
5042 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 13.

5044 is a value of n for which

φ(n) and σ(n) are square.
5046 is the first of five consecutive

squareful numbers.
5048 is the number of

strongly connected digraphs with 5 vertices.
5049 is an octagonal pyramidal number.

5050 is the sum of the first 100

integers.
5054 = 555 + 0 + 55 + 4444.

5055 has exactly the same digits in 3 different bases.

5056 is the number of ways to flip a coin 13 times and get at least 3 heads in a row.

5057 is the number of squares in a 16×16 grid of squares with diagonals drawn.

5059 is the number of inequivalent asymmetric

Ferrers graphs with 33 points.
5061 is a number n whose 5

^{th} root has a decimal part that begins with the digits of n.

5069 is the number of

square-free graphs with 10 vertices.
5071 is a

Lucas 3-step number and a Lucas 4-step number.
5077 has a

square whose digits each occur twice.
5078 is the number of rectangles with corners on an 12×12 grid of points.

5080 is a structured truncated octahedral number.

5083 is an centered icosahedral number.

5084 is the number of inequivalent

Ferrers graphs with 33 points.
5087 has an eleventh root whose decimal part starts with the digits 1-9 in some order.

5088 divides the sum of the digits of 2

^{5088} × 5088!.

5096 is the number of possible rook moves on a 14×14 chessboard.

5098 is the number of

3-valent trees with 17 vertices.
5100 is divisible by its reverse.

5103 and its successor are both divisible by 4

^{th} powers.

5104 is the smallest number that can be written as the sum of 3

cubes in 3 ways.
5105 would be

prime if preceded and followed by a 1, 3, 7, or 9.
5107 preceded by 5107 1's is

prime.
5108 is the number of different flushes in 5 card poker.

5109 is the number of

conjugacy classes of the alternating group A_{33}.
5118 is the maximum value of n so
that there exist 6 denominations of stamps so that every postage from 1
to n can be paid for with at most 12 stamps.

5120 is the number of edges in a 10 dimensional

hypercube.
5130 is a value of n for which

φ(n) and σ(n) are square.
5133 is the smallest integer ratio of a 18-digit number to its product of digits.

5134 has the property that the sum of the

factorials of its digits is its largest prime factor.
5135 is not the sum of a

square, a cube, a 4^{th} power, and a 5^{th} power.
5136 does not occur in its

factorial in base 2.
5141 is the sum of the first 17 numbers that have digit sum 17.

5141 is the only four digit number that is reversed in

hexadecimal.
5142 is the sum of its

proper divisors that contain the digit 7.
5143 = 555 + 111 + 4444 + 33.

5146 has a base 3 representation that begins with its base 7 representation.

5152 is the number of legal rook moves in Chess.

5153 is an Eisenstein-Mersenne

prime.
5160 is a hendecagonal pyramidal number.

5161 = 5! + (1+6)! + 1!

5162 = 5! + (1+6)! + 2.

5163 = 5! + (1+6)! + 3.

5164 = 5! + (1+6)! + 4.

5165 = 5! + (1+6)! + 5.

5166 = 5! + (1+6)! + 6.

5167 = 5! + (1+6)! + 7.

5168 has a

square root that has four 8's immediately after the decimal point.
5169 = 5! + (1+6)! + 9.

5170 is the number of

partitions of 39 that do not contain 1 as a part.
5172 has a

cube whose last few digits are ...48848448.
5174 has a 4

^{th} power containing only 4 different digits.

5176 is the number of labeled

graphs with 6 vertices that have chromatic number 2.
5177 is the number of labeled

bipartite graphs with 6 vertices.
5180 is the smallest number whose 7

^{th} power has 26 digits.

5181 is a structured octagonal anti-diamond number.

5182 is a number whose sum of

divisors is a 5^{th} power.
5183 is the product of

twin primes.
5184 is the number of ways to place 2 non-attacking rooks on a 9×9 chessboard.

5185 is the number of 2×2

singular matrices mod 17.
5186 is equal to the sum of its

anti-divisors.
5187 is the only number n known for which

φ(n-1) = φ(n) = φ(n+1).
5191 is a value of n for which

σ(n+1) = 2σ(n).
5199 divides the sum of the

cubes of the first 5199 primes.
5200 is divisible by its reverse.

5204 has the property that if each digit is replaced by its

square, the resulting number is a square.
5211 has a

square root whose decimal part starts with the digits 1-9 in some order.
5216 is a structured hexagonal diamond number.

5218 is the number of

3-colorable graphs connected graphs with 8 vertices.
5220 = 1111 in base 17.

5222 has the property that the sum of the n

^{th} powers of its digits is prime for 1 ≤ n &\le 9.

5225 is the number of ways to color the vertices of a triangle with 25 colors, up to rotation.

5226 is the number of ways to color the vertices of a square with 12 colors, up to rotation.

5229 uses the same digits as

φ(5229).
5234 has a

cube that is only 17 away from a square.
5237 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5239 has a

square whose digits each occur twice.
5241 is the starting location of 7777 in the decimal expansion of

π.
5242 is the number of ways to place 8 non-attacking kings on a 8×8 chessboard so that there is a king in every row and column.

5244 is the sum of consecutive

squares in 2 ways.
5247 is the number of ordered ways to write 1 as a sum of reciprocals of

integers no larger than 10.
5248 is the number of ordered ways to write 1 as a sum of reciprocals of

integers no larger than 11.
5250 is the number of linear geometries on 10 unlabeled points.

5252 is the maximum number of regions space can be divided into by 26

spheres.
5256 is the number of labeled

partially ordered sets of 4 elements.
5257 is a member of the

Fibonacci-type sequence starting with 1 and 8.
5258 has a base 8 representation which is the reverse of its base 7 representation.

5260 is the number of

multigraphs with 24 vertices and 4 edges.
5264 is the smallest number so that it and its successor are both the product of 2

primes and the 4^{th} power of a prime.
5265 is a

Rhonda number.
5269 is the number of

binary rooted trees with 18 vertices.
5271 is a value of n for which 2n and 7n together use each digit exactly once.

5274 is the sum of its

proper divisors that contain the digit 7.
5278 is the number of ways, up to symmetry, to pick 3 elements of an 8×8 grid.

5279 is the number

permutations of {1,2,3,...,20} where adjacent numbers differ by no more than 2.
5280 is the number of feet in a mile.

5281 has a 4

^{th} power that is the sum of four 4

^{th} powers.

5282 is the number of different arrangements (up to rotation and reflection) of 8 non-attacking

rooks on a 8×8 chessboard.
5284 and the two numbers before it and after it are all products of exactly 3

primes.
5289 is a structured rhombic triacontahedral number.

5291 is a value of n for which n(n+1) is a

palindrome.
5292 = 28 + 0 + 0 + 5264 and has

square 28005264.
5293 is the smallest number that ends an arithmetic progression of 12 numbers with the same

prime signature.
5296 is the

Entringer number E(8,3).
5306 is the smallest number whose 9

^{th} power starts with 4 identical digits.

5309 has the property that if each digit is replaced by its

square, the resulting number is a square.
5312 is the index of a

prime Woodall number.
5313 is the index of a

triangular number containing only 3 different digits.
5314 is a value of n for which |cos(n)| is smaller than any previous

integer.
5322 is the starting location of 7777 in the decimal expansion of

π.
5324 is the number of binary

cube-free words of length 20.
5327 is a value of n for which 2n and 7n together use each digit exactly once.

5328 is the number of one-sided 6-knights.

5332 is a

Kaprekar constant in base 3.
5335 is the magic constant of a 22×22 magic square.

5336 is a house number.

5340 is an

octahedral number.
5346 = 198 × 27 and each digit is contained in the equation exactly once.

5349 = 12345 in base 8.

5355 is an odd

primitive abundant number.
5357 is the smallest number that can not be formed using the digit 1 at most 27 times, together with the symbols +, –, × and ÷.

5358 are the first 8 digits of

π^{5358}.
5362 is the number of Chess positions that can be reached after 2 moves by white and 1 move by black.

5364 is a value of n for which 3n and 7n together use each digit exactly once.

5366 is the number of

graphs with 8 vertices that have chromatic number 4.
5367 uses the same digits as

φ(5367).
5369 is a

Wolstenholme number.
5371 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5376 is the order of a

perfect group.
5382 is the number of non-intersecting rook paths joining opposite corners of a 6×4 chessboard.

5383 is the number of triangles of any size contained in the triangle of side 27 on a triangular grid.

5387 is the index of a

prime Fibonacci number.
5390 is the number of ways to 7-color the faces of a

cube.
5392 is a

Leyland number.
5399 has a

cube whose digits occur with the same frequency.
5400 is divisible by its reverse.

5401 is a member of the

Fibonacci-type sequence starting with 3 and 7.
5405 is the smaller number in a

Ruth-Aaron pair.
5406 is the number of ways a 9×1 rectangle can be surrounded by 9×1 rectangles.

5408 is an

Achilles number.
5409 and its reverse are both differences of positive

cubes.
5412 is a value of n so that n(n+4) is a

palindrome.
5414 is the number of binary

partitions of 43.
5418 is a value of n for which n and 7n together use each digit 1-9 exactly once.

5419 is a

Cuban prime.
5422 is the number of

semigroups of order 6 with 3 idempotents.
5431 is the smallest number whose 4

^{th} power contains 5 consecutive 9's.

5432 has digits in

arithmetic sequence.
5434 is the sum of consecutive

squares in 2 ways.
5436 is the number of terms in the 10

^{th} derivative of f(f(f(f(f(x))))).

5439 is a

Rhonda number.
5440 is the number of ways to legally add 2 sets of parentheses to a product of 15 variables.

5443 is the smallest

prime p with 17 consecutive quadratic residues mod p.
5446 is the number of ways to to arrange the numbers 1-10 around a circle so that the sums of adjacent numbers are distinct.

5448 is the number of ways to cut a 10×10 chessboard into 2 pieces with equal areas with a cut that only travels up and right.

5455 is a

Kaprekar number for cubes.
5456 and its reverse are

tetrahedral numbers.
5457 is a number whose sum of

divisors is a 5^{th} power.
5460 is both a

triangular number and 7 times a triangular number.
5461 is a

Poulet number.
5462 is the number of ways to walk along 14 edges of a triangle and end at the original vertex.

5463 has a 4

^{th} power that is the sum of four 4

^{th} powers.

5464 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 12.

5469 has the property that

e^{5469} is within .00003 of an integer.
5471 contains no 0's in base 3 through base 10.

5472 has a base 3 representation that ends with its base 4 representation.

5473 has a base 3 representation that ends with its base 4 representation.

5474 is a

stella octangula number.
5477 and its reverse are both one more than a

square.
5478 is the number of

graphs with 10 vertices that have chromatic number 2.
5479 is the number of

bipartite graphs with 10 vertices.
5482 is the number of 3×3 sliding puzzle positions that require exactly 16 moves to solve starting with the hole in the center.

5483 is the number of unlabeled

distributive lattices with 18 elements.
5487 is the maximum number of pieces a

torus can be cut into with 31 cuts.
5488 is an

Achilles number.
5489 is the maximum number of regions a

cube can be cut into with 32 cuts.
5491 has a 4

^{th} power that is the sum of four 4

^{th} powers.

5493 is the number of

integers with complexity 30.
5499 is the average of all the even 4-digit numbers.

5504 is the number of series-parallel networks with 6 labeled edges.

5505 is a value of n for which n

!!! - 1 is prime.
5507 has a

square root whose decimal part starts with the digits 0-9 in some order.
5508 is the

generalized Catalan number C(13,5).
5509 is the number of

multigraphs with 8 vertices and 9 edges.
5513 is the number of

self-avoiding walks of length 10.
5525 is the smallest number that can be written as the sum of 2

squares in 6 ways.
5530 is a

hexagonal pyramidal number.
5533 is the number of

graphs with 10 vertices and 2 cycles.
5536 is the 16

^{th} Tetranacci number.
5542 is the number of

anisohedral 19-ominoes.
5543 has a 4

^{th} power that is the sum of four 4

^{th} powers.

5544 is the number of

permutations of 9 items that fix 4 elements.
5545 is a member of the

Fibonacci-type sequence starting with 1 and 5.
5551 is the number of

trees on 17 vertices with diameter 6.
5554 is a

Kaprekar number for cubes.
5555 is a

repdigit.
5557 contains no 0's in base 3 through base 10.

5560 are the first 4 digits of 7

^{5560}.

5561 has the property that the sum of its

prime factors is equal to the product of its digits.
5564 is an

amicable number.
5565 is a doubly triangular numbers.

5566 is a

pentagonal pyramidal number.
5568 is the number of ways to put 8
checkers on an 8×8 checkerboard so that each row, column, and main
diagonal contains exactly one checker.

5571 is a

perfect totient number.
5573 is the number of digits in the 6

^{th} Cullen prime.
5574 is the number of

trees on 31 vertices with diameter 4.
5576 is a decagonal pyramidal number.

5585 is the number of

monoids of order 7 with 2 idempotents.
5586 does not occur in its

factorial in base 2.
5587 has a 5

^{th} root that starts 5.61611166....

5588 is the index of a

triangular number containing only 3 different digits.
5591 is the smallest

prime that is followed by 31 composite numbers.
5594 is the number of ways to dissect a 14-gon using non-crossing diagonals into polygons with an even number of sides.

5595 is the number of labeled mappings from 6 points to themselves with exactly 3 cycles.

5597 has a

cube with only odd digits.
5600 is the number of

self-complementary graphs with 13 vertices.
5602 = 22222 in base 7.

5604 is the number of

partitions of 30.
5610 is divisible by its reverse.

5611 is the smallest number for which it and the 3 numbers before and after it all have

φ(n) divisible by 10.
5612 has the property that dropping its first and last digits gives its largest

prime factor.
5616 is the order of a

non-cyclic simple group.
5617 is a

divisor of the sum of the 4^{th} powers of its divisors.
5619 has a

cube that contains the digits 5619 in reverse order.
5620 is the smallest

composite number which remains composite when preceded or followed by any digit.
5623 and the

primes preceding it and following it are all equal to 7 (mod 16).
5624 is the number of binary 5×5 matrices up to permutations of rows and columns.

5625 has a

cube that is the sum of 3 positive cubes.
5629 is the maximum value of n so
that there exist 5 denominations of stamps so that every postage from 1
to n can be paid for with at most 16 stamps.

5637 uses the same digits as

φ(5637).
5638 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole in a corner.

5647 is the closest

integer to 24^{e}.
5651 is a number n for which n, n+2, n+6, and n+8 are all

prime.
5661 is the

trinomial coefficient T(18,14).
5664 is a

Rhonda number.
5668 is the number of

semigroups of order 6 with 5 idempotents.
5669 is a value of n for which |cos(n)| is smaller than any previous

integer.
5670 is a value of n for which

φ(n) and σ(n) are square.
5671 is a

triangular number that is the product of two primes.
5673 is the smallest number whose 6

^{th} power starts with 5 identical digits.

5675 is the number of

monic polynomials of degree 13 with integer coefficients whose complex roots are all in the unit disk.
5678 has digits in

arithmetic sequence.
5679 is the number of drawings of the

complete graph K_{10} with a minimal number of crossings.
5680 is a value of n for which n

!!!! + 1 is prime.
5682 is the sum of its

proper divisors that contain the digit 4.
5689 is the largest 4-digit

prime with strictly increasing digits.
5690 is the number of isomers of C

_{13}H

_{26} containing a double bond.

5691 is the number of different resistances that can be created in a circuit of 11 equal resistors.

5692 is a number that does not have any digits in common with its

cube.
5693 = 5555 + 6 + 99 + 33.

5694 = 17082 / 3, and each digit is contained in the equation exactly once.

5696 is the smallest number whose

square contains 4 consecutive 4's.
5697 has a 21

^{st} power that contains five 5's, six 6's, nine 9's, and seven 7's.

5698 is the smallest number whose 8

^{th} power starts with 5 identical digits.

5700 is divisible by its reverse.

5709 is a structured pentakis dodecahedral number.

5711 is the smallest

prime p with 18 consecutive quadratic residues mod p.
5712 is the number of

Gray codes for a 4-dimensional cube.
5717 is a value of n for which the first n binary digits of

π form a prime.
5718 is the number of

partitions of 54 into distinct parts.
5719 is a

Zeisel number.
5720 is a dodecagonal pyramidal number.

5721 is the number of

graphs with 8 vertices that have chromatic number 3.
5723 has the property that its

square starts with its reverse.
5729 has a 4

^{th} power that is the sum of four 4

^{th} powers.

5731 is a value of n for which n (n+2) is a

palindrome.
5734 has a

square that is a centered pentagonal number.
5737 is the smallest number that can not be formed using the digit 1 at most 22 times, together with the symbols +, × and ^.

5739 is a value of n for which 5n and 7n together use each digit exactly once.

5740 = 7777 in base 9.

5741 is the 11

^{th} Pell number.
5742 is a value of n for which 5n and 8n together use each digit exactly once.

5751 is the number of ordered sequences of coins totaling 31 cents.

5754 is the number of ways a loop can cross two parallel lines a total of 12 times.

5755 is the sum of the digits of the 19

^{th} Mersenne prime.
5760 is the order of a

perfect group.
5767 is the product of two consecutive

primes.
5768 is the 16

^{th} tribonacci number.
5769 is the number of

permutations of 9 elements that have 3^{rd} power equal to the identity permutation.
5770 is a value of n for which

φ(n) and σ(n) are square.
5772 are the first 4 decimal digits of

Euler's constant.
5773 is the index of a

triangular number containing only 3 different digits.
5774 is the smallest number whose

square begins with four 3's.
5775 is the smallest value of n for which both n and n+1 are

abundant.
5776 is the square of the last half of its digits.

5777 is the smallest multi-digit number which is not the sum of a

prime and twice a square.
5778 is the largest

Lucas number which is also a triangular number.
5781 is a centered tetrahedral number.

5784 has a

square whose digits each occur twice.
5786 = 5555 + 77 + 88 + 66.

5789 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5790 has the same digits as the 5790

^{th} prime.
5791 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5793 are the first 4 digits of 5793

^{e}.

5795 is a value of n such that the n

^{th} Cullen number is prime.
5796 = 138 × 42 and each digit is contained in the equation exactly once.

5798 is the 11

^{th} Motzkin number.
5807 is the index of a

Wagstaff prime.
5813 is the concatenation of 3 consecutive

Fibonacci numbers.
5814 =

_{19}P_{3}.
5817 = 34902 / 6, and each digit is contained in the equation exactly once.

5818 contains no 0's in base 3 through base 10.

5819 has a sum of digits equal to its largest

prime factor.
5821 contains no 0's in base 3 through base 10.

5822 is the number of

conjugacy classes in the automorphism group of the 16 dimensional hypercube.
5823 is the smallest value of n for which n and 3n together use each digit 1-9 exactly once.

5824 can be written as the difference between two positive

cubes in more than one way.
5825 are the first 4 digits of e

^{5825}.

5830 is a

weird number.
5831 has a sum of digits equal to its largest

prime factor.
5832 is a value of n for which n and 3n together use each digit 1-9 exactly once.

5834 is the number of digits of the 21

^{st} perfect number.
5839 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5842 is a

Padovan number.
5843 has a 5

^{th} root that starts 5.66666....

5844 is the number of ways to stack 34 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

5848 has a

square that remains square when a 9 is appended to it.
5850 is a value of n for which n-1 and n+1 are

twin primes, and so are 2n-1 and 2n+1.
5851 is a value of n for which n, n

^{2}, and n

^{3} have the same digit sum.

5853 is the index of a

triangular number containing only 3 different digits.
5856 = 1 × 6 × 16 × 61.

5858 has a

square whose digits each occur twice.
5859 can be written as the difference between two positive

cubes in more than one way.
5860 is the sum of the

squares of 4 consecutive primes.
5863 is the starting location of 7777 in the decimal expansion of

π.
5864 has a 14

^{th} power that contains five 5's, eight 8's, six 6's, and four 4's.

5865 is an enneagonal pyramidal number.

5867 is a member of the

Fibonacci-type sequence starting with 1 and 9.
5868 is a value of n for which n, n

^{2}, and n

^{3} have the same digit sum.

5870 has a digit sum smaller than its

cube.
5872 = 5555 + 88 + 7 + 222.

5873 divides 1

^{1} + 2

^{2} + 3

^{3} +

^{ . . .} + 5873

^{5873}.

5876 is the number of ways to color the vertices of a triangle with 26 colors, up to rotation.

5877 is a value of n for which 5n and 8n, or 8n and 9n, together use each digit exactly once.

5879 is the smallest number so that it and the next 10 numbers all have an odd number of

prime factors.
5880 is the

Stirling number of the second kind S(10,7).
5885 is a number whose sum of

divisors is a 5^{th} power.
5886 is a value of n for which 3n and 5n together use each digit exactly once.

5890 is a

heptagonal pyramidal number.
5892 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5895 is the number of necklaces possible with 7 beads, each being one of 5 colors.

5896 is the number of ways to tile a 3×24 rectangle with 3×1 rectangles.

5900 is the number of ways to place 32 points on a 16×16 grid so that

no 3 points are on a line.
5904 has a

square comprised of the digits 1-8.
5906 is the smallest number which is the sum of 2 rational 4

^{th} powers but is not the sum of two

integer 4^{th} powers.
5909 is the number of symmetric

plane partitions of 32.
5913 = 1! + 2! + 3! + 4! + 5! + 6! + 7!

5914 = 0! + 1! + 2! + 3! + 4! + 5! + 6! + 7!

5915 is the sum of consecutive

squares in 2 ways.
5916 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5921 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5923 is the largest n so that

**Q**(√n) has class number 7.
5925 is the index of a

triangular number containing only 3 different digits.
5926 +

φ(5926) = 8888.
5929 is a

square which is also the sum of 11 consecutive squares.
5931 is the number of one-sided

7-kings.
5934 is a value of n for which 5n and 7n together use each digit exactly once.

5935 is a

Smith brother.
5936 is divisible by the digits it does not contain, and not divisible by the digits it contains.

5938 is the number of binary

partitions of 44.
5939 is the smallest

prime so that it and the next 2 primes are all equal to 3 (mod 7).
5940 is divisible by its reverse.

5941 is the number of interior intersections when all the diagonals of a

regular 22-gon are drawn.
5943 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.
5950 is the sum of the digits of the 20

^{th} Mersenne prime.
5953 and the

primes preceding it and following it are all equal to 3 (mod 14).
5958 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 11.

5959 is the smaller number in a

Ruth-Aaron pair.
5960 is the larger number in a

Ruth-Aaron pair.
5963 is the number of intersections when all the diagonals of a

regular 22-gon are drawn.
5967 is a value of n for which 6n and 7n together use each digit exactly once.

5968 has a

square which uses the digits 0-7 each exactly once.
5972 is the smallest number that appears in its

factorial 8 times.
5974 is the number of

connected planar graphs with 8 vertices.
5975 is a value of n for which

σ(n) = σ(reverse(n)).
5976 is a value of n for which n and 7n together use each digit 1-9 exactly once.

5978 is a value of n where

φ(n) is the product of the digits of n.
5984 =

_{34}C_{3}.
5985 =

_{21}C_{4}.
5986 and its

prime factors contain every digit from 1-9 exactly once.
5993 is the largest number known which is not the sum of a

prime and twice a square.
5994 is the number of

lattices on 10 unlabeled nodes.
5995 is a

palindromic triangular number.
5996 is a

truncated tetrahedral number.
5999 is the smallest number whose digits add to 32.

6000 is the number of subsets of the 24

^{th} roots of unity that add to 1.
6001 has a

cube that is a concatenation of other cubes.
6002 is the number of digits of the 24

^{th} Mersenne prime.
6003 has a

square with the first 3 digits the same as the next 3 digits.
6006 is the number of intersections when all the diagonals of a

regular 21-gon are drawn.
6008 =

_{14}C_{6} + _{14}C_{0} + _{14}C_{0} + _{14}C_{8}.
6009 is a

strobogrammatic number.
6011 is a member of the

Fibonacci-type sequence starting with 3 and 8.
6012 has a

square with the last 3 digits the same as the 3 digits before that.
6014 has a

square that is formed by 3 squares that overlap by 1 digit.
6016 is the maximum number of pieces a

torus can be cut into with 32 cuts.
6017 is a centered octahedral number.

6018 is the maximum number of regions a

cube can be cut into with 33 cuts.
6020 is the number of

Hamiltonian graphs with 8 vertices.
6021 has a

square that is formed by 3 squares that overlap by 1 digit.
6024 is a value of n for which |cos(n)| is smaller than any previous

integer.
6025 are the last 4 digits of the sum of the first 6025

squares.
6032 is the number of ways to place 2 non-attacking

knights on a 9×9 chessboard.
6035 is a number whose sum of

divisors is a 5^{th} power.
6040 is the number of ways to divide 6 couples into pairs where no pair is a couple.

6048 is the order of a

non-cyclic simple group.
6050 has a sum of digits equal to its largest

prime factor.
6058 is a number that does not have any digits in common with its

cube.
6065 is the closest

integer to 16^{π}.
6070 is a structured truncated tetrahedral number.

6072 is the order of a

non-cyclic simple group.
6073 is the order of a

non-cyclic simple group.
6075 is an

Achilles number.
6077 has a

square with the last 3 digits the same as the 3 digits before that.
6080 is the smallest number n>1 whose base 14 representation is equal to

φ(n).
6081 has a

cube that is the sum of 3 positive cubes.
6083 has a

square that is the sum of a cube and a 4^{th} power.
6084 is the sum of the first 12

cubes.
6092 is the number of

16-ominoes with a line of symmetry.
6093 is a value of n for which 3n and 5n together use each digit exactly once.

6095 is a

rhombic dodecahedral number.
6097 is an hexagonal prism number.

6099 concatenated with its successor is

square.
6100 has the property that if each digit is replaced by its

square, the resulting number is a square.
6102 is the largest number n known where

φ(n) is the reverse of n.
6105 is a

Huay rhombic dodecahedral number.
6106 is a value of n for which 2

φ(n) = φ(n+1).
6107 is a

Perrin number.
6111 is a value of n for which

σ(n-1) = σ(n+1).
6119 is a

strobogrammatic number.
6120 is a highly abundant number.

6121 is the smallest number whose

cube contains 4 consecutive 3's.
6128 is a

betrothed number.
6137 is a centered dodecahedral number.

6138 is the number of quasi-

tetrominoes that fit inside a 7×7 grid.
6141 is a

Kaprekar constant in base 2.
6142 is the number of inequivalent asymmetric

Ferrers graphs with 34 points.
6143 is the smallest prime that contains twelve 1's in binary.

6144 = 16

!!!!.
6145 is a

Friedman number.
6153 is the number of

partitions of 40 that do not contain 1 as a part.
6155 is a member of the

Fibonacci-type sequence starting with 2 and 5.
6164 is the number of

11-ominoes that tile the plane using 180 degree rotations.
6167 has a 4

^{th} power that is the sum of four 4

^{th} powers.

6168 is the number of inequivalent

Ferrers graphs with 34 points.
6170 = 5 + 55 + 555 + 5555.

6171 has the property that dropping its first and last digits gives its largest

prime factor.
6173 is a

prime that remains prime if any digit is deleted.
6174 is the

Kaprekar constant for 4-digit numbers.
6175 is the number of regions formed when all diagonals are drawn in a

regular 21-gon.
6176 is the last 4-digit sequence to appear in the decimal expansion of

π.
6179 is a value of n for which 4n and 5n together use each digit exactly once.

6180 is the smallest number n with

φ(n) = 2 reverse(n).
6181 is an

octahedral number.
6187 is a

Smith brother.
6188 =

_{17}C_{5}.
6189 is the number of ways to write 17 as an ordered sum of positive

integers, where adjacent numbers are different.
6194 is the number of ways to place a non-attacking white and black pawn on a 10×10 chessboard.

6196 is the number of regions the

complex plane is cut into by drawing lines between all pairs of 21^{st} roots of unity.
6197 is a

narcissistic number in base 6.
6200 is a

harmonic divisor number.
6201 is the sum of the first 26

squares.
6210 is the number of 5×5 matrices with non-negative entries with every row and column adding to 2.

6211 is a

Cuban prime.
6216 has a

square with the first 3 digits the same as the next 3 digits.
6219 is a value of n for which 4n and 5n together use each digit exactly once.

6220 = 44444 in base 6.

6221 = 666 + 2222 + 2222 + 1111.

6222 is the smallest number that can not be written as the sum of 2

triangular numbers and a power of 2.
6223 = 666 + 2222 + 2 + 3333.

6224 is the number of

permutations of 8 elements that have 4^{th} power equal to the identity permutation.
6225 = 666 + 2 + 2 + 5555.

6232 is an

amicable number.
6235 is the number of different resistances that can be formed by eleven or fewer 1-ohm resistors in series or parallel.

6237 is a number whose sum of the

squares of its divisors is a square.
6239, followed by 6239 7's, is

prime.
6240 is a highly abundant number.

6244 is a member of the

Fibonacci-type sequence starting with 2 and 9.
6245 is the smallest number whose

square contains 4 consecutive internal 0's.
6248 is the smallest number with the property that its first 8 multiples contain the digit 4.

6249 is the smallest number with the property that its first 10 multiples contain the digit 4.

6250 is a

Leyland number.
6256 is a hendecagonal pyramidal number.

6257 is the number of essentially different ways to dissect a

20-gon into 9 quadrilaterals.
6266 is a

truncated octahedral number.
6267 is the number of

15-iamonds with holes.
6270 is a value of n for which n-1 and n+1 are

twin primes, and so are 2n-1 and 2n+1.
6271 is the smallest number requiring an

addition chain of length 17.
6272 is the number of ways to tile a 4×29 rectangle with 4×1 rectangles.

6273 is the number of ways to 9-color the vertices of a pentagon, up to rotations and reflections.

6274 has a

cube whose digits occur with the same frequency.
6276 is a value of n for which

φ(n) = φ(reverse(n)).
6279 is the number of subsequences of {1,2,3,...14} in which every odd number has an even neighbor.

6280 has a sum of

prime factors that is equal to the sum of the prime factors of the two preceding numbers.
6290 is the number of

13-iamonds that do not tile the plane.
6293 is the number of ordered

partitions of 24 into distinct parts.
6296 has a

square with the first 3 digits the same as the next 3 digits.
6297 is a value of n for which n and 5n together use each digit 1-9 exactly once.

6299 is the smallest number with

complexity 30.
6300 is divisible by its reverse.

6307 is the largest n so that

**Q**(√n) has class number 8.
6309 is the closest

integer to 25^{e}.
6310 is the smallest number whose 5

^{th} power has 19 digits.

6312 is the sum of its

proper divisors that contain the digit 5.
6318 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
6320 is the

Entringer number E(8,4).
6322 is the number of

idempotent functions from a set of 7 elements into itself.
6327 = 324 + 325 + . . . + 342 = 343 + 344 + . . . + 360.

6331 has the same digits as the 6331

^{st} prime.
6332 is the number of

fullerenes with 68 carbon atoms.
6336 is the number of ways to tile a 9×4 rectangle with 2×1 rectangles.

6343 is the number of quasi-

triominoes that fit inside a 14×14 grid.
6347 has the same digits as the 6347

^{th} prime.
6348 is a

pentagonal pyramidal number.
6351 is the largest number known that is not the sum of 3

squares or cubes.
6354 is the number of

14-iamonds that tile the plane.
6360 is a value of n for which n-1 and n+1 are

twin primes, and so are 3n-1 and 3n+1.
6368 is an

amicable number.
6371 has a

square that is the sum of 2 relatively prime cubes.
6374 is a value of n for which 4n and 5n together use each digit exactly once.

6375 has a

square with the first 3 digits the same as the next 3 digits.
6378 is the number of

partitions of 55 into distinct parts.
6379 is a value of n for which |cos(n)| is smaller than any previous

integer.
6380 is a value of n for which n! + 1 is

prime.
6381 is the smallest value of n for which n and 9n together use each digit 1-9 exactly once.

6384 is an icosahedral number.

6385 is the number of ways to stack 18 pennies in a line so that each penny lies on the table or on two pennies.

6389 is the number of

functional graphs on 11 vertices.
6391 is a

hexagonal pyramidal number.
6395 is the number of ways to divide a 12×12 grid of points into two sets using a straight line.

6396 is a

divisor of the sum of the 4^{th} powers of its divisors.
6397 has the same digits as the 6397

^{th} prime.
6399 and its successor are both divisible by 4

^{th} powers.

6400 is a

square whose digits are non-increasing.
6403 has a

square with the first 3 digits the same as the last 3 digits.
6404 is a value of n for which n

!! - 1 is prime.
6406 is the number of

permutations of 8 elements where every cycle has equal length.
6408 is the sum of the

squares. of the first 13 primes.
6409 is a house number.

6411 is a truncated cube number.

6424 is the number of

minimal covers of a set containing 6 elements.
6427 is the number of ways a 6×6 square can be tiled with 1×1 and 2×2 squares.

6432 has the same digits as the 6432

^{nd} prime.
6434 is the number of

divisors of the 18^{th} perfect number.
6435 =

_{15}C_{7}.
6440 is a value of n for which n

!!!! + 1 is prime.
6443 has a

cube whose digits occur with the same frequency.
6444 is the smallest number whose 5

^{th} power starts with 5 identical digits.

6445, followed by 6445 1's, is

prime.
6454 is the smallest value of n for which

π(10n) = n.
6455 is the smallest value of n for which the n

^{th} prime begins with the digits of n.
6456 is a value of n for which the n

^{th} prime begins with the digits of n.
6457 is a value of n for which the n

^{th} prime begins with the digits of n.
6458 would be

prime if preceded and followed by a 1, 3, 7, or 9.
6459 is a value of n for which the n

^{th} prime begins with the digits of n.
6460 is a value of n for which the n

^{th} prime begins with the digits of n.
6462 divides the sum of the digits of 6462!.

6466 is the largest known value of n for which the n

^{th} prime begins with the digits of n.
6471 is a value of n for which n and 9n together use each digit 1-9 exactly once.

6472 is the number of

polyominoes with 9 or fewer squares.
6475 is a value of n for which

π(n) is the product of the digits of n.
6479 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6481 = (3

^{12} + 1) / (3

^{4} + 1).

6487 is the number of

partitions of 51 in which no part occurs only once.
6488 would be

prime if preceded and followed by a 1, 3, 7, or 9.
6489 is half again as large as the sum of its proper

divisors.
6490 is the number of ways to place 2 non-attacking

bishops on a 11×11 chessboard.
6498 is the index of a

triangular number containing only 3 different digits.
6500 is a number n whose sum of the

factorials of its digits is equal to π(n).
6501 has a

square whose reverse is also a square.
6505 is the number of

9-hexes without holes.
6506 is a value of n for which the first n binary digits of

π form a prime.
6510 is a number n whose sum of the

factorials of its digits is equal to π(n).
6511 is a number n whose sum of the

factorials of its digits is equal to π(n).
6512 is the number of 11-ominoes that tile the plane

isohedrally.
6514 is the sum of the 4

^{th} powers of the digits of the sum of the 4

^{th} powers of the digits of itself.

6517 has a sum of digits equal to its largest

prime factor.
6521 is a number n whose sum of the

factorials of its digits is equal to π(n).
6523 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
6524 has the property that its

square starts with its reverse.
6525 is a centered icosahedral number.

6526 is the smallest number whose 10

^{th} power contains exactly the same digits as another 10

^{th} power.

6527 is a value of n for which

φ(n) = φ(n-1) + φ(n-2).
6529 is a

Proth prime.
6532 is a member of the

Fibonacci-type sequence starting with 1 and 6.
6533 is the number of digits of the 25

^{th} Mersenne prime.
6534 is a value of n for which 3n and 7n together use each digit exactly once.

6537 is the smallest value of n for which the numbers n-6 through n+6 can not be written as the sum of 2

squares.
6540 is the number of terms in the 17

^{th} derivative of f(f(f(x))).

6543 has a

square root that has four 8's immediately after the decimal point.
6544 is a number n whose 9

^{th} root has a decimal part that begins with the digits of n.

6545 and its reverse are

tetrahedral numbers.
6547 is the number of binary 4×4 matrices with no row or column containing 3 consecutive 1's.

6552 is the number of different full houses in 5 card poker with one joker.

6553 is a

Lucas 5-step number.
6556 is the largest

palindrome that can be made using 5 digits and the 4 arithmetic operations.
6557 is the product of two consecutive

primes.
6560 is the smallest number n where n and n+1 are both products of 7 or more

primes.
6561 = 3

^{8}.

6569 is a value of n for which one less than the product of the first n

primes is prime.
6572 is the number of

9-hexes.
6576 = (6! - 6) + (5! - 5) + (7! - 7) + (6! - 6).

6578 is the smallest number which can be written as the sum of three 4

^{th} powers in 2 ways.

6579 is the number of ways to color the vertices of a triangle with 27 colors, up to rotation.

6580 is the maximum number of regions a

cube can be cut into with 34 cuts.
6581 has the same digits as the 6581

^{st} prime.
6583 is a value of n for which

σ(φ(n)) = 2σ(n).
6586 is a value of n for which n

!!!! + 1 is prime.
6588 is the number of sided

12-iamonds.
6593 = 6 + 5555 + 999 + 33.

6594 is a value of n for which 5n and 7n together use each digit exactly once.

6596 has a

square comprised of the digits 0-7.
6601 is a

Carmichael number.
6603 is a number whose

square and cube use different digits.
6608 is the maximum number of regions space can be divided into by 28

spheres.
6609 has a 4

^{th} power that is the sum of four 4

^{th} powers.

6611 is a value of n such that the n

^{th} Cullen number is prime.
6615 is an odd

abundant number.
6620 is the number of

11-ominoes that tile the plane.
6623 has the property that the sum of its

prime factors is equal to the product of its digits.
6630 is the number of triangles of any size contained in the triangle of side 29 on a triangular grid.

6636 has exactly the same digits in 3 different bases.

6639 divides 1

^{1} + 2

^{2} + 3

^{3} +

^{ . . .} + 6639

^{6639}.

6642 can be written as the sum of 2 or 4 positive 4

^{th} powers.

6643 is the smallest number which is

palindromic in bases 2 and 3.
6647 has a sum of digits equal to its largest

prime factor.
6651 is the index of a

triangular number containing only 3 different digits.
6653, when concatenated with 4 less than itself, is

square.
6654 is the smallest number whose decimal part of its 4

^{th} root starts with the digits 0-9 in some order.

6663 is a value of n for which

σ(n) is a repdigit.
6665 is a centered tetrahedral number.

6666 is a

repdigit.
6667 is the number of self-dual

planar graphs with 24 edges.
6668 is the number of

trees on 21 vertices with diameter 5.
6669 is the sum of 3 consecutive

cubes.
6680 = 6666 + 6 + 8 + 0.

6681 = 6666 + 6 + 8 + 1.

6682 = 6666 + 6 + 8 + 2.

6683 = 6666 + 6 + 8 + 3.

6684 = 6666 + 6 + 8 + 4.

6685 = 6666 + 6 + 8 + 5.

6686 = 6666 + 6 + 8 + 6.

6687 = 6666 + 6 + 8 + 7.

6688 = 6666 + 6 + 8 + 8.

6689 = 6666 + 6 + 8 + 9.

6694 is a value of n for which the sum of the first n

primes is square.
6699 is a

strobogrammatic number.
6700 has a

cube that contains the digits 6700 in reverse order.
6704 is the number of rooted

8-hexes.
6706 is the number of

Hamiltonian paths in a 8×5 rectangle graph.
6712 is the index of a

triangular number containing only 3 different digits.
6714 is the index of a

triangular number containing only 3 different digits.
6716 is the 4-digit string that appears latest in the decimal expansion of

π.
6720 =

_{8}P_{5}.
6721 is a

composite value of n that divides the (n-1)^{st} Fibonacci number.
6723 is a value of n for which 3n and 8n together use each digit exactly once.

6726 is the 10

^{th} Pell-Lucas number.
6728 is the number of domino tilings of a 6×6 square.

6729 is the smallest value of n for which n and 2n together use each digit 1-9 exactly once.

6731 would be

prime if preceded and followed by a 1, 3, 7, or 9.
6732 is a value of n for which

_{2n}C_{n} is divisible by n^{2}.
6734 is a value of n for which |cos(n)| is smaller than any previous

integer.
6735 is a

stella octangula number.
6736 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole in the center.

6740 is the number of

13-iamonds that do not tile the plane.
6741 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6742 has a

square where the first 6 digits alternate.
6743 is the number of binary 4×5 matrices with no consecutive 1's in any row or column.

6745 is the maximum value of n so
that there exist 4 denominations of stamps so that every postage from 1
to n can be paid for with at most 25 stamps.

6751 is the number of digits of the 23

^{rd} perfect number.
6754 is the smallest number in base 9 to have 5 different digits.

6756 has a

cube that is the sum of 3 positive cubes.
6757 is the number of

connected graphs with 10 vertices and 34 edges.
6759 is the number of

graphs with 10 vertices and 11 edges.
6764 is the sum of the first 18

Fibonacci numbers.
6765 is the 20

^{th} Fibonacci number.
6768 has a 9

^{th} root that starts 2.664444666....

6769 is the

Stirling number of the first kind s(8,4).
6772 has a

square whose digits each occur twice.
6779 = 6666 + 7 + 7 + 99.

6780 has the same digits as the 6780

^{th} prime.
6786 is a

triangular number whose internal digits are triangular and whose external digits are triangular.
6788 is the smallest number with

multiplicative persistence 6.
6789 is the largest 4-digit number with increasing digits.

6791 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6792 is a value of n for which n and 2n together use each digit 1-9 exactly once.

6793 is the smallest

prime so that it and the next 2 primes all end in 3.
6794 has the property that dropping its first and last digits gives its largest

prime factor.
6797 is a number whose sum of

divisors is a 5^{th} power.
6799 is the number of different

degree sequences possible for a graph with 18 edges.
6801 has a 4

^{th} power that is the sum of four 4

^{th} powers.

6802 is the number of ways to move a rook from corner to opposite corner on a 6×6 chessboard.

6811 is not the sum of a

square, a cube, a 4^{th} power, and a 5^{th} power.
6813 is the smallest number whose 6

^{th} power has 24 digits.

6816 is the index of a

triangular number containing only 3 different digits.
6818 = 1

^{8} + 2

^{8} + 3

^{8}.

6819 = 20457 / 3, and each digit is contained in the equation exactly once.

6820 is the number of regions formed when all diagonals are drawn in a

regular 23-gon.
6822 uses the same digits as

φ(6822).
6825 is an odd

primitive abundant number.
6828 is the number of ways to start with a knight in the corner of an 8×8 chessboard, make 8 moves, and end on the same square.

6831 is a structured truncated octahedral number.

6837 is the number of 8-digit

squares.
6839 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6840 is the number of ways to place 2 non-attacking kings on a 11×11 chessboard.

6842 is the number of

partitions of 31.
6845 would be

prime if preceded and followed by a 1, 3, 7, or 9.
6849 is a value of n for which 2n and 3n together use each digit exactly once.

6850 is the smallest value of n for which n, n+1, n+2, n+3, n+4, and n+5 have the same number of

prime factors.
6853 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.
6859 = 19

^{3}.

6860 is a

heptagonal pyramidal number.
6861 is a value of n for which

σ(n-1) + σ(n+1) = σ(2n).
6863 is a

prime that is the sum of the square of a prime and the cube of a prime.
6864 = 6666 + 88 + 66 + 44.

6865 is the maximum value of n so
that there exist 5 denominations of stamps so that every postage from 1
to n can be paid for with at most 17 stamps.

6867 can be written as the sum of 2, 3, 4, or 5 positive

cubes.
6868 is the larger number in a

Ruth-Aaron pair.
6874 is equal to the sum of its

anti-divisors.
6875 is

3-automorphic.
6879 is the number of planar partitions of 15.

6880 is a

vampire number.
6886 is a

palindrome in base 9 and in base 10.
6888 has a

square with 3/4 of the digits are the same.
6889 is a

strobogrammatic square.
6895 is a value of n for which 2n and 7n together use each digit exactly once.

6896 has a

square root whose decimal part starts with the digits 0-9 in some order.
6900 is the number of ways to place 2 non-attacking

knights on a 11×11 chessboard.
6902 is the number of

Hamiltonian paths of a 3×10 rectangle graph.
6903 is a value of n for which

σ(n-1) = σ(n+1).
6905 has a 5

^{th} root whose decimal part starts with the digits 1-9 in some order.

6912 = 6 × 9 × 1 × 2

^{7}.

6917 is a value of n for which n! - 1 is

prime.
6918 = 20754 / 3, and each digit is contained in the equation exactly once.

6919 is the number of

non-invertible knots with 13 crossings.
6922 is the number of

polycubes containing 8 cubes.
6924 is the magic constant of a 24×24 magic square.

6926 has a

square whose digits each occur twice.
6927 is a value of n for which n and 2n together use each digit 1-9 exactly once.

6928 is the number of inequivalent binary

linear codes of length 11.
6930 is the

square root of a triangular number.
6931 has the same digits as the 6931

^{st} prime.
6935 is the smallest number whose

cube contains six 3's.
6936 is the number of ways to legally add 2 sets of parentheses to a product of 16 variables.

6939 is a value of n for which 3n and 5n together use each digit exactly once.

6940 is the sum of its

proper divisors that contain the digit 3.
6941 has a

square whose digits each occur twice.
6942 is the number of labeled

topologies with 5 elements.
6944 is the number of

degree sequences for graphs with 6 vertices.
6949 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with

integer dimensions less than 16.
6951 has exactly the same digits in 3 different bases.

6952 = 1738 × 4 and each digit from 1-9 is contained in the equation exactly once.

6953 = 66 + 999 + 5555 + 333.

6954 is the

trinomial coefficient T(19,15).
6956 is the number of triangles formed by drawing all diagonals of a

regular 12-gon.
6960 is the number of ways to place 2 non-attacking queens on a 10×10 chessboard.

6966 is the number of

planar graphs with 8 vertices.
6969 is a

strobogrammatic number.
6972 is the number of possible positions in Checkers containing 2 checkers.

6976 is the number of binary 5×5 matrices A with the property that A

^{2}=0 (mod 2).

6982 is a value of n for which the sum of the first n

composite number numbers is a square.
6983 is the smallest

prime that can only be made into 1 other prime by changing a single digit.
6984 can be written as the sum of 2, 3, 4, or 5 positive

cubes.
6985 is the smallest number that can be written as the sum of 3 or more consecutive

squares, or as the sum of 3 or more consecutive cubes.
6987 is the number of digits of the 26

^{th} Mersenne prime.
6989 has the property that the concatenation of its

prime factors in increasing order is a square.
6991 is a value of n for which reverse(

φ(n)) = φ(reverse(n)).
6996 is a

palindrome n so that n(n+8) is also palindromic.
6998 is a member of the

Fibonacci-type sequence starting with 4 and 9.
6999 is the smallest number whose digits add to 33.

7000 has a sum of digits equal to its largest

prime factor.
7001 is the number of

13-hexes that tile the plane by translation.
7002 is the number of arrangements of 4 non-attacking

queens on a 8×8 chessboard.
7003 is the number of

graphs with 9 vertices that have 8 automorphisms.
7014 has a

square with the last 3 digits the same as the 3 digits before that.
7015 has a

cube root whose decimal part starts with the digits 1-9 in some order.
7019 is a

prime that remains prime if any digit is deleted.
7028 is the smallest multi-digit number n, when written in base 17, gives a divisor of n.

7030 is an octagonal pyramidal number.

7032 is the number of

ternary square-free words of length 24.
7039 = 28156 / 4, and each digit is contained in the equation exactly once.

7040 has a sum of digits equal to its largest

prime factor.
7055 is a

Lucas-Carmichael number.
7056 is a

square that is the product of two triangular numbers.
7057 is a

Cuban prime.
7060 has the property that the sum of the

squares of its divisors ends with the digits 7060.
7066 is the maximum value of n so
that there exist 6 denominations of stamps so that every postage from 1
to n can be paid for with at most 13 stamps.

7068 is the number of

series-reduced planted trees with 11 leaves.
7071 is the smallest number whose

square contains 4 consecutive 9's.
7072 is the

generalized Catalan number C(10,7).
7073 is a

Leyland number.
7075 is the number of ways to stack 35 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

7084 is the

generalized Catalan number C(19,4).
7089 is a value of n for which |cos(n)| is smaller than any previous

integer.
7092 is the number of possible positions in Othello after 3 moves by both players.

7093 has a 6

^{th} root that starts 4.38333833....

7094 is the number of ways to place 34 points on a 17×17 grid so that

no 3 points are on a line.
7096 is the number of 8-digit perfect powers.

7098 is the

trinomial coefficient T(14,9).
7101 has a 4

^{th} power that is the sum of four 4

^{th} powers.

7102 is the index of a

Fibonacci number whose first 9 digits are the digits 1-9 rearranged.
7106 is an

octahedral number.
7107 has a

square whose digits each occur twice.
7108 is the number of

partitions of 56 into distinct parts.
7117 is a number whose sum of

divisors is a 5^{th} power.
7119 has the same digits as the 7119

^{th} prime.
7120 is the number of 2×2

singular matrices mod 10.
7122 = 7

^{2} + 8

^{3} + 9

^{4}.

7123 is the number of

2-connected graphs with 8 vertices.
7140 is the largest number which is both

triangular and tetrahedral.
7142 is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with

integer dimensions less than 20.
7143 is

7-automorphic.
7145 has a

square with the first 3 digits the same as the next 3 digits.
7150 has a sum of digits equal to its largest

prime factor.
7152 has a

square with the first 3 digits the same as the next 3 digits.
7159 has a

square with the first 3 digits the same as the next 3 digits.
7161 is a

Kaprekar constant in base 2.
7164 is a value of n for which n

^{8}, n

^{9}, n

^{10}, and n

^{11} have the same digit sum.

7170 is a value of n for which

σ(n-1) = σ(n+1).
7172 is a

Kaprekar number for cubes.
7174 is the maximum number of pieces a

torus can be cut into with 34 cuts.
7175 is a centered octahedral number.

7176 is the maximum number of regions a

cube can be cut into with 35 cuts.
7187 is the smallest number that can not be formed using the digits 0-8 at most once, together with the symbols +, –, × and ÷.

7188 is the number of ways to permute 5 red, 5 white, and 5 blue balls.

7189 is the number of ways to color the vertices of a square with 13 colors, up to rotation.

7192 is a

weird number.
7193 is a

right-truncatable prime.
7197 is the smallest number whose 7

^{th} power has 27 digits.

7200 is the order of a

perfect group.
7201 is the number of 2×2

singular matrices mod 19.
7209 has a 4

^{th} power that is the sum of four 4

^{th} powers.

7212 is the number of unordered ways to write 1 as a sum of reciprocals of

integers no larger than 20.
7225 is the number of ways to 17-color the faces of a

tetrahedron.
7226 has a

cube root that starts 19.3330030330....
7230 is the sum of consecutive

squares in 2 ways.
7235 is a value of n for which 4n and 5n together use each digit exactly once.

7236 uses the same digits as

φ(7236).
7240 = 1111 in base 19.

7241 is the number of asymmetric

trees with 19 vertices.
7245 appears inside its 4

^{th} power.

7248 is the number of lines through exactly 2 points of a 14×14 grid of points.

7253 has a

square that remains square when a 6 is appended to it.
7254 = 186 × 39 and each digit is contained in the equation exactly once.

7256 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.
7260 is a doubly triangular numbers.

7269 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7271 and its reverse are both differences of positive

cubes.
7272 is a

Kaprekar number.
7281 is a value of n for which 3n and 7n together use each digit exactly once.

7285 has a 7

^{th} power that contains the same digits as 544

^{10}.

7286 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 9.

7293 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7295 is a value of n for which 4n and 5n together use each digit exactly once.

7297 is a

Proth prime.
7306 is the smallest number whose 7

^{th} power starts with 7 identical digits.

7311 is the number of symmetric

plane partitions of 33.
7312 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7314 is the smallest number so that it and its successor are both products of 4 distinct

primes.
7315 =

_{22}C_{4}.
7318 is the number of functions from 10 unlabeled points to themselves.

7320 is the number of triangles of any size contained in the triangle of side 30 on a triangular grid.

7321 is the number of intersections when all the diagonals of a

regular 24-gon are drawn.
7322 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole on a side.

7326 = 1 × 22 × 333.

7327 is a number whose sum of

divisors is a 5^{th} power.
7329 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7330 is the number of unsymmetrical ways to dissect a

regular 14-gon into 12 triangles.
7331 is a

right-truncatable prime.
7333 is a

right-truncatable prime.
7336 is the number of ways to color the vertices of a triangle with 28 colors, up to rotation.

7337 is a

hexagonal pyramidal number.
7338 is the closest

integer to 17^{π}.
7339 has a 4

^{th} power that is the sum of four 4

^{th} powers.

7341 has the same digits as the 7341

^{st} prime.
7342 is the number of ways to stack 29 pennies in contiguous rows so that each penny lies on the table or on two pennies.

7344 is a value of n for which 4n and 7n together use each digit exactly once.

7345 has the same digits as the 7345

^{th} prime.
7351 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
7353 is the largest number n known so that both n and n

^{3} have only odd digits.

7356 is a value of n for which 5n and 7n together use each digit exactly once.

7358 is a

composite number that remains composite when preceded or followed by any digit.
7359 is a

Lucas 6-step number.
7360 can be written as the product of a number and its reverse in 2 different ways.

7361 is the number of ways to play the first 5 moves in Checkers.

7364 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7366 is the maximum number of regions space can be divided into by 29

spheres.
7371 has a base 2 representation that begins with its base 9 representation.

7375 is a member of the

Fibonacci-type sequence starting with 1 and 4.
7376 is a structured truncated tetrahedral number.

7380 is the number of numbers with 4 or fewer digits that do not contain any 0's.

7381 = 11111 in base 9.

7383 has a 4

^{th} power that is 1/2 of the sum of three 4

^{th} powers.

7384 has the same digits as the 7384

^{th} prime.
7385 is a

Keith number.
7387 is the product of two consecutive

primes.
7393 is a

right-truncatable prime.
7396 has a 4

^{th} root whose decimal part starts with the digits 1-9 in some order.

7403 is the smallest number that can not be formed using the digit 1 at most 28 times, together with the symbols +, –, × and ÷.

7404 = 6 + 66 + 666 + 6666.

7410 = 361 + 362 + . . . + 380 = 381 + 382 + . . . + 399.

7413 is the number of

even permutations on 8 elements with no fixed points.
7414 is a value of n for which

φ(n) = φ(reverse(n)).
7416 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7420 is the number of

permutations of 8 items that fix 2 elements.
7421 is a value of n for which 4n and 5n together use each digit exactly once.

7422 is the sum of its

proper divisors that contain the digit 7.
7424 and its successor are both

abundant.
7425 is an odd

primitive abundant number.
7427 is the number of inequivalent asymmetric

Ferrers graphs with 35 points.
7429 is the product of 3 consecutive

primes.
7430 is the number of labeled

commutative monoids of order 5.
7433 is a

prime that remains prime if any digit is deleted.
7435 is a cubic star number.

7436 is the number of 6×6

alternating sign matrices.
7444 is a value of n for which |cos(n)| is smaller than any previous

integer.
7447 is a

palindrome in base 2 and in base 10.
7448 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
7456 is the number of inequivalent

Ferrers graphs with 35 points.
7462 is the number of

multigraphs with 26 vertices and 4 edges.
7464 is a structured hexagonal diamond number.

7465 = 54321 in base 6.

7469 is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with

integer dimensions less than 21.
7471 is a

centered cube number.
7473 is a

Tribonacci-like number starting from 1, 1, and 1.
7475 has a sum of digits equal to its largest

prime factor.
7480 is a value of n for which

_{2n}C_{n} is divisible by n^{2}.
7485 is the number of

conjugacy classes of the alternating group A_{35}.
7488 = (12 × 13 × 14 × 15 × 16) / (12 + 13 + 14 + 15 + 16) .

7490 has a

square with the last 3 digits the same as the 3 digits before that.
7491 has a base 8 representation which is the reverse of its base 7 representation.

7494 is the sum of its

proper divisors that contain the digit 4.
7496 = 777 + 44 + 9 + 6666.

7497 is a hendecagonal pyramidal number.

7499 is the smallest number whose 8

^{th} power has 31 digits.

7500 is the order of a

perfect group.
7508 would be

prime if preceded and followed by a 1, 3, 7, or 9.
7509 has a 6

^{th} root whose decimal part starts with the digits 1-9 in some order.

7512 is the sum of its

proper divisors that contain the digit 5.
7515 has the property that the sum of its

prime factors is equal to the product of its digits.
7519 is a member of the

Fibonacci-type sequence starting with 1 and 7.
7524 is the number of rectangles with corners on an 12×12 grid of points.

7525 has a

square with the last 3 digits the same as the 3 digits before that.
7528 is the number of ways, up to rotation and reflection, of dissecting a

regular 14-gon into 12 triangles.
7531 has digits in

arithmetic sequence.
7532 has a

square comprised of the digits 0-7.
7535 has a

square whose digits each occur twice.
7541 is an Eisenstein-Mersenne prime.

7542 is a value of n for which 4n and 7n together use each digit exactly once.

7546 is the number of

series-reduced planted trees with 19 vertices.
7547 is the maximum number of regions a circle can be cut into by joining 21 points on the circumference with straight lines.

7549 is the largest known

prime p where no numbers of the form p-n^{2} are prime.
7551 is a value of n for which

φ(n) + φ(n+1) divides σ(n) + σ(n+1).
7552 is the number of arrangements of 6 non-attacking

queens on a 10×6 chessboard.
7557 is a

palindrome that is the sum of the first 37 palindromes.
7560 is the smallest number with 64

divisors.
7561 is a

Markov number.
7562 would be

prime if preceded and followed by a 1, 3, 7, or 9.
7574 is the sum of consecutive

squares in 2 ways.
7581 is the number of monotone

Boolean functions of 5 variables.
7586 = 777 + 55 + 88 + 6666.

7588 is the smallest multiple of 28 whose digits add to 28.

7590 is a number whose sum of

divisors is a 4^{th} power.
7595 is the number of simplicial

polyhedra with 12 vertices.
7597 is a number whose sum of

divisors is a 5^{th} power.
7600 is a substring of any power of itself.

7614 is a value of n for which n and 7n together use each digit 1-9 exactly once.

7615 is a value of n for which

σ(n+1) = 2σ(n).
7617 is a

Hexanacci number.
7618 has a

cube that contains only digits 4 and smaller.
7620 is the number of

multigraphs with 5 vertices and 14 edges.
7625 is a value of n for which

σ(φ(n)) = 2σ(n).
7627 is a value of n for which

σ(φ(n)) = 2σ(n).
7629 is a value of n for which n and 5n together use each digit 1-9 exactly once.

7632 is a value of n for which 5n and 6n together use each digit exactly once.

7635 is a centered tetrahedral number.

7639 is the number of

rooted ternary trees with 13 vertices.
7647 is a

Keith number.
7648 is the number of ways a 10×1 rectangle can be surrounded by 10×1 rectangles.

7650 can be written as the product of a number and its reverse in 2 different ways.

7651 is a value of n for which

_{2n}C_{n} is not divisible by 3, 5, or 7.
7652 is a value of n for which n

^{2} and n

^{3} use the same digits.

7654 has digits in

arithmetic sequence.
7658 is the largest number known that does not have any digits in common with its

cube.
7659 is the number of

planar graphs with 22 vertices, all with degree 5 or more.
7663 is the product of two

primes which are reverses of each other.
7664 is the

Entringer number E(8,6).
7665 is a

Kaprekar constant in base 2.
7667 is a

palindrome in base 6 and in base 10.
7669 is the number of

integers with complexity 31.
7672 = 777 + 6666 + 7 + 222.

7673 is the smallest number with the property that its first 8 multiples contain the digit 3.

7679 = 7 + 6666 + 7 + 999.

7680 is the number of possible rook moves on a 16×16 chessboard.

7681 is a

Proth prime.
7683 is a

truncated tetrahedral number.
7685 is the number of necklaces possible with 18 beads, each being one of 2 colors.

7686 is a value of n for which 7n and 9n together use each digit exactly once.

7688 is an

Achilles number.
7692 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7693 is a value of n for which the sum of the first n

primes is a palindrome.
7695 and its successor are both divisible by 4

^{th} powers.

7698 has a

square with the first 3 digits the same as the next 3 digits.
7700 is a value of n for which 2

φ(n) = φ(n+1).
7703 has a 4

^{th} power that is the sum of four 4

^{th} powers.

7710 is the number of degree 17

irreducible polynomials over GF(2).
7712 is the number of necklaces (that can't be turned over) possible with 17 beads, each being one of 2 colors.

7713 is a value of n for which 4n and 9n together use each digit exactly once.

7714 is the sum of the first 28

squares.
7721 is the smallest value of n for which 3

^{n} contains 8 consecutive 3's.

7724 is the smallest number that can not be written using +, ×, and 5

Fibonacci numbers.
7727 is the index of a

Fibonacci number whose first 9 digits are the digits 1-9 rearranged.
7732 and the two numbers before it and after it are all products of exactly 3

primes.
7734 is the sum of its

proper divisors that contain the digit 8.
7736 is the number of labeled

Eulerian digraphs with 5 vertices.
7738 has the property that dropping its first and last digits gives its largest

prime factor.
7739 is a

Padovan number.
7741 is the number of

trees with 15 vertices.
7743 is the smallest number whose 9

^{th} power has 35 digits.

7744 is the smallest known

square with no isolated digits.
7745 and its reverse are both one more than a

square.
7746 is the number

permutations of {1,2,3,...,21} where adjacent numbers differ by no more than 2.
7752 is the

generalized Catalan number C(14,5).
7754 is the number of binary

cube-free words of length 21.
7755 is the index of a

prime Woodall number.
7765 is the number of ways to tile a 7×5 rectangle with

integer-sided squares.
7770 =

_{37}C_{3}.
7772 has a

square root whose decimal part starts with the digits 1-9 in some order.
7773 is the number of stable patterns with 17 cells in Conway's game of

Life.
7775 = 55555 in base 6.

7776 is a 5

^{th} power whose digits are non-increasing.

7777 is a

Kaprekar number.
7778 is the closest

integer to 27^{e}.
7785 is a value of n for which 5n and 6n together use each digit exactly once.

7788 is the index of a

triangular number containing only 3 different digits.
7792 has a

square that is the sum of a cube and 5^{th} power.
7793 is the smallest

prime so that it and the next 5 primes are all equal to 5 (mod 6).
7795 has the same digits as the 7795

^{th} prime.
7799 is a value of n for which |cos(n)| is smaller than any previous

integer.
7800 is the order of a

non-cyclic simple group.
7803 is an

Achilles number.
7805 is the maximum number of pieces a

torus can be cut into with 35 cuts.
7807 is the maximum number of regions a

cube can be cut into with 36 cuts.
7808 is the number of 4×4 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner.

7810 has the property that its

square is the concatenation of two consecutive numbers.
7811 is the number of ordered sequences of coins totaling 32 cents.

7812 = 222222 in base 5.

7820 is the

Stirling number of the second kind S(17,15).
7821 is a value of n for which 2n and 9n together use each digit exactly once.

7824 is a value of n for which 5n and 7n together use each digit exactly once.

7825 is a

rhombic dodecahedral number.
7826 is the number of necklaces possible with 6 beads, each being one of 6 colors.

7827 has a

square whose digits each occur twice.
7835 would be

prime if preceded and followed by a 1, 3, 7, or 9.
7846 is a factor of 7847784878497850.

7848 is the number of

connected 5-regular graphs with 12 vertices.
7849 is the number of

connected 6-regular graphs with 12 vertices.
7851 = 7777 + 8 + 55 + 11.

7852 = 1963 × 4, and each digit from 1-9 is contained in the equation exactly once.

7853 is the largest

prime factor of 11! - 1.
7854 is a number whose sum of

divisors is a 4^{th} power.
7856 and its successor are both the product of a

prime and the 4^{th} power of a prime.
7860 is the number of

nonisomorphic 3-state automata with binary inputs and outputs.
7874 is the smallest number n for which n concatenated with n+2 is a

square.
7875 is an odd

abundant number.
7880 is the maximum value of n so
that there exist 4 denominations of stamps so that every postage from 1
to n can be paid for with at most 26 stamps.

7882 is a structured pentagonal hexacontahedral number.

7884 is a value of n for which 2n and 5n together use each digit exactly once.

7887 is the index of a

pentagonal number which is twice another pentagonal number.
7888 is a value of n where

φ(n) is the product of the digits of n.
7890 is an icosahedral number.

7894 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7895 is the number of

multigraphs with 6 vertices and 11 edges.
7905 is a

Kaprekar constant in base 2.
7908 has the same digits as the 7908

^{th} prime.
7909 is a

Keith number.
7912 is a

weird number.
7913 is a value of n for which

σ(n-1) = σ(n+1).
7917 is the number of

partitions of 57 into distinct parts.
7919 is the 1000

^{th} prime.
7920 is the order of the smallest

sporadic group.
7921 is the

square of a Fibonacci number.
7922 has the property that the sum of its

prime factors is equal to the product of its digits.
7923 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7926 is the diameter of the earth in miles.

7928 is a

Friedman number.
7931 is a

heptagonal pyramidal number.
7932 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7936 is the 5

^{th} tangent number.
7937 is the smallest number whose

cube contains 5 consecutive 9's.
7939, when followed by any of its digits, is

prime.
7941 = 7777 + 9 + 44 + 111.

7942 = 7777 + 99 + 44 + 22.

7946 = 7777 + 99 + 4 + 66.

7953 is the number of domino tilings of a 3×14 rectangle.

7954 is the smallest value of n for which 5

^{n} + n is

prime.
7956 is a value of n for which n and 4n together use each digit 1-9 exactly once.

7957 is a

Poulet number.
7958 = 8 × 9 × 10 × 11 + 8 + 9 + 10 + 11.

7960 is a structured deltoidal hexacontahedral number.

7964 is a value of n for which

φ(n) = φ(reverse(n)).
7969 has a

square that is formed by 3 squares that overlap by 1 digit.
7980 is the smallest number whose

divisors contain every digit at least 7 times.
7983 is a

Lucas 8-step number.
7986 = 11 × 22 × 33.

7992 can be written as the difference between two positive

cubes in more than one way.
7993 is one less than twice its reverse.

7994 has a 5

^{th} power that is closer to a

cube than a square.
7997 is a

palindrome in base 4 and in base 10.
7999, when followed by any of its digits, is

prime.
8000 is the smallest

cube which is also the sum of 4 consecutive cubes.
8001 is a

Kaprekar constant in base 2.
8002 is the index of a

triangular number containing only 3 different digits.
8003 has the property that if each digit is replaced by its

square, the resulting number is a square.
8004 has a

square with the first 3 digits the same as the next 3 digits.
8008 =

_{16}C_{6}.
8010 uses the same digits as

π(8010).
8012 is the number of

3-connected planar maps with 18 edges.
8016 has a

square with the last 3 digits the same as the 3 digits before that.
8022 uses the same digits as

φ(8022).
8026 is the number of

planar partitions of 19.
8032 is the number of congruency classes of triangles with vertices from a 15×15 grid of points.

8042 is the largest number known which cannot be written as a sum of 7 or fewer

cubes.
8043 has a

square whose digits each occur twice.
8045 is the number of 6-digit

twin primes.
8051 is the number of

partitions of 52 in which no part occurs only once.
8056 is the number of triangles of any size contained in the triangle of side 31 on a triangular grid.

8064 = (1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9) / (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9).

8071 is the number of

connected graphs with 11 edges.
8074 is the

trinomial coefficient T(12,6).
8077 is a value of n for which n

^{2} and n

^{3} use the same digits.

8080 has a

square root that has four 8's immediately after the decimal point.
8082 has a

square comprised of the digits 1-8.
8083 is a value of n for which n concatenated with n-2 is

square.
8085 is an odd

primitive abundant number.
8087 is a

Lucas 9-step number.
8089 is the

pseudosquare modulo 13.
8090 is a

Perrin number.
8092 is a

Friedman number.
8100 is divisible by its reverse.

8103 is the closest

integer to e^{9}.
8104 is equal to the sum of its

anti-divisors.
8118 is a

strobogrammatic number.
8119 is an

NSW number.
8121 is the smallest number whose

cube contains seven 5's.
8125 is the smallest number that can be written as the sum of 2

squares in 5 ways.
8128 is the 4

^{th} perfect number.
8129 is a member of the

Fibonacci-type sequence starting with 2 and 7.
8135 is the 7

^{th} central pentanomial coefficient.

8136 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
8149 is a value of n for which 2n and 7n together use each digit exactly once.

8152 is the number of symmetric arrangements of 8 non-attacking

queens on a 8×8 chessboard.
8154 is a value of n for which |cos(n)| is smaller than any previous

integer.
8156 has a

cube that is only 24 away from a square.
8165 has a

square that begins with four 6's.
8169 = 24507 / 3, and each digit is contained in the equation exactly once.

8170 is an enneagonal pyramidal number.

8174 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8176 is a

stella octangula number.
8178 is the number of ways 13 people can line up so that only one person has a taller person in front of him.

8179 is a value of n for which 4n and 5n together use each digit exactly once.

8180 is the maximum number of regions space can be divided into by 30

spheres.
8184 has exactly the same digits in 3 different bases.

8189 is the index of a

triangular number containing only 3 different digits.
8190 is a

harmonic divisor number.
8191 is a

Mersenne prime.
8192 is the smallest non-trivial 13

^{th} power.

8194 is the number of subsets of the 26

^{th} roots of unity that add to 0.
8195 is the number of

17-ominoes with a horizontal or vertical line of symmetry.
8196 has a

square whose digits each occur twice.
8198 is the index of a

Fibonacci number whose first 9 digits are the digits 1-9 rearranged.
8200 = 8 + 2

^{13} + 0 + 0.

8201 = 8 + 2

^{13} + 0 + 1.

8202 = 8 + 2

^{13} + 0 + 2.

8203 = 8 + 2

^{13} + 0 + 3.

8204 = 8 + 2

^{13} + 0 + 4.

8205 = 8 + 2

^{13} + 0 + 5.

8206 = 8 + 2

^{13} + 0 + 6.

8207 = 8 + 2

^{13} + 0 + 7.

8208 is a

narcissistic number.
8209 = 8 + 2

^{13} + 0 + 9.

8217 is a centered icosahedral number.

8219 is a value of n for which 4n and 5n together use each digit exactly once.

8220 and its reverse are both the averages of

twin primes.
8221 has a base 3 representation that begins with its base 6 representation.

8225 are the first 4 digits of 8

^{8225}.

8226 is the sum of its

proper divisors that contain the digit 4.
8229 has a

square whose digits each occur twice.
8230 is the number of necklaces with 8 beads, each one of 4 colors.

8241 is a value of n for which n has

σ(n) / reverse(n) divisors.
8242, when concatenated with one less than it, is

square.
8256 is the number of different arrangements (up to rotation and reflection) of 30 non-attacking

bishops on a 16×16 chessboard.
8257 is the sum of the

squares. of the first 14 primes.
8258 is the number of different positions in Connect Four after 6 moves.

8265 has a 7

^{th} root whose decimal part starts with the digits 1-9 in some order.

8269 is a

Cuban prime.
8280 is the smaller number in a

Ruth-Aaron pair.
8281 is the only 4-digit

square whose two 2-digit pairs are consecutive.
8283 has a base 8 representation which is the reverse of its base 7 representation.

8284 is a structured truncated cubic number.

8292 is the number of

anisohedral 22-iamonds.
8294 has the property that dropping its first and last digits gives its largest

prime factor.
8299 is a value of n for which reverse(

φ(n)) = φ(reverse(n)).
8303 = 12345 in base 9.

8304 is the number of subsets of the 18

^{th} roots of unity that add to a real number.
8305 has the same digits as the 8305

^{th} prime.
8313 is a dodecagonal pyramidal number.

8316 is the sum of 3 consecutive

cubes.
8317 is the number of

trees on 33 vertices with diameter 4.
8320 is the number of subsets of {1, 1/2, 1/3, ... 1/42} that sum to an

integer.
8321 is a

Poulet number.
8338 is a value of n so that n(n+4) is a

palindrome.
8340 is a value of n so that (n-1)

^{2} + n

^{2} + (n+1)

^{2} is a

palindrome.
8342 is the number of

partitions of 53 in which no part occurs only once.
8345 is the smallest number in base 6 to have 6 different digits.

8349 is the number of

partitions of 32.
8350 is the

trinomial coefficient T(10,1).
8351 has the same digits as the 8351

^{st} prime.
8353 is the smallest number whose 4

^{th} power contains 5 consecutive 6's.

8355 has the same digits as the 8355

^{th} prime.
8360 has a

square whose digits each occur twice.
8361 is a

Leyland number.
8363 is the number of 5-digit

primes.
8368 has a 6

^{th} power whose first few digits are 34334444....

8369 is the largest

prime factor of 2 × 3 × 5 × 7 × 11 × 13 × 17 - 1.
8372 is a

hexagonal pyramidal number.
8373 has a 4

^{th} power that is the sum of four 4

^{th} powers.

8375 is the smallest number which has equal numbers of every digit in bases 2 and 6.

8378 has a 10

^{th} root whose decimal part starts with the digits 1-9 in some order.

8379 is a value of n for which 5n and 8n together use each digit exactly once.

8382 is the index of a

triangular number containing only 3 different digits.
8384 is the maximum number of 13

^{th} powers needed to sum to any number.

8385 is a structured great rhombicubeoctahedral number.

8388 and its reverse are both the averages of

twin primes.
8390 is the number of linear spaces on 7 labeled points.

8392 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.
8393 is a value of n for which

σ(reverse(n)) = φ(n).
8394 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8396 does not occur in its

factorial in base 2.
8397 is the largest known

composite number n so that _{3n}C_{n} = 3^{n} (mod n).
8398 is the 10

^{th} super-ballot number.

8400 is the number of legal queen moves in Chess.

8401 has the property that if each digit is replaced by its

square, the resulting number is a square.
8403 = 33333 in base 7.

8404 is the number of

connected graphs with 9 vertices and 13 edges.
8406 is the number of ways to divide 8 black and 8 white beads into piles.

8408 has 8408 /

π(8408) divisors.
8411 would be

prime if preceded and followed by a 1, 3, 7, or 9.
8415 is an odd

primitive abundant number.
8418 is the number of necklaces possible with 11 beads, each being one of 3 colors.

8419 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8420 is the number of symmetric ways to fold a strip of 20 stamps.

8421 = 1111 in base 20.

8428 is the number of quasi-

triominoes that fit inside a 15×15 grid.
8430 and its reverse are both the averages of

twin primes.
8433 has a 4

^{th} power that is the sum of four 4

^{th} powers.

8436 =

_{38}C_{3}.
8439 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8440 is a truncated square pyramid number.

8441 is the sum of the

cubes of 3 consecutive primes.
8442 is the smallest value of n for which the numbers n-7 through n+7 can not be written as the sum of 2

squares.
8451 is the number of 3×3 matrices in base 3 with

determinant 0.
8455 is the

trinomial coefficient T(20,16).
8459 is a value of n so that n(n+4) is a

palindrome.
8461 is the smallest number whose 9

^{th} power starts with 5 identical digits.

8463 is the smaller number in a

Ruth-Aaron pair.
8464 is the number of different products of subsets of the set {1, 2, 3, ... 17}.

8465 = 4

^{3} + 5

^{4} + 6

^{5}.

8467 has a 9

^{th} root whose decimal part starts with the digits 1-9 in some order.

8469 is a value of n for which 2n and 3n together use each digit exactly once.

8470 is the number of

conjugacy classes in the automorphism group of the 17 dimensional hypercube.
8472 is the maximum number of pieces a

torus can be cut into with 36 cuts.
8473 is a centered octahedral number.

8474 is the maximum number of regions a

cube can be cut into with 37 cuts.
8475 is the first of four consecutive

squareful numbers.
8477 = 1

^{0} + 2

^{1} + 3

^{2} + 4

^{3} + 5

^{4} + 6

^{5}.

8481 is a

Poulet number.
8484 is the

reciprocal of the sum of the reciprocals of 13332 and its reverse.
8486 = 888 + 44 + 888 + 6666.

8492 is the number of arrangements of 5 non-attacking

queens on a 11×5 chessboard.
8493 has a 4

^{th} power that is the sum of four 4

^{th} powers.

8494 is a value of n for which

σ(n) = φ(n) + φ(n-1) + φ(n-2).
8497 is the number of

anisohedral 17-hexes.
8499 is the sum of the

squares of 3 consecutive primes.
8505 = 21

!!!!!!.
8506 is the number of isomers of C

_{13}H

_{26} without any double bonds.

8509 is a value of n for which |cos(n)| is smaller than any previous

integer.
8510 is a value of n for which the sum of the first n

primes is a palindrome.
8512 is the number of non-intersecting rook paths joining opposite corners of a 5×5 chessboard.

8515 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
8517 has a 4

^{th} power that is the sum of four 4

^{th} powers.

8521 is a

prime that is the average of two 4^{th} powers.
8523 is the first of four consecutive

squareful numbers.
8525 has a

square whose digits each occur twice.
8526 is a

Rhonda number.
8533 has the property that dropping its first and last digits gives its largest

prime factor.
8538 is the sum of its

proper divisors that contain the digit 4.
8541 is a value of n so that n(n+6) is a

palindrome.
8545 is the number of ways to stack 36 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

8547 is a

divisor of 111111.
8548 is the sum of the

squares of 4 consecutive primes.
8549 has the property that the sum of its

proper divisors is the sum of the squares of its digits.
8555 is the sum of the first 29

squares.
8558 is a

Schröder number.
8559 has a

square comprised of the digits 1-8.
8562 is the sum of its

proper divisors that contain the digit 4.
8563 is the index of a

triangular number containing only 3 different digits.
8568 =

_{18}C_{5}.
8569 is a centered dodecahedral number.

8571 shares 3 consecutive digits with one of its

prime factors.
8575 is an

Achilles number.
8576 can be written as the sum of 2, 3, 4, or 5 positive

cubes.
8577 has a 4

^{th} power that is the sum of four 4

^{th} powers.

8578 appears inside its 4

^{th} power.

8579 divides 1

^{1} + 2

^{2} + 3

^{3} +

^{ . . .} + 8579

^{8579}.

8580 is the number of subsets of the 28

^{th} roots of unity that add to 1.
8582 is the number of

monoids of order 7 with 5 idempotents.
8586 has exactly the same digits in 3 different bases.

8591 is the number of

partitions of 42 that do not contain 1 as a part.
8599 is the number of

forests with 14 vertices.
8602 is the

generalized Catalan number C(20,4).
8610 = 400 + 401 + . . . + 420 = 421 + 422 + . . . + 440.

8614 and its

prime factors contain every digit from 1-9 exactly once.
8626 is the number of asymmetric

trees with 13 vertices.
8627 is a value of n for which 2n and 7n together use each digit exactly once.

8631 is a value of n for which 3n and 7n together use each digit exactly once.

8633 is the product of two consecutive

primes.
8637 has a 4

^{th} power that is the sum of four 4

^{th} powers.

8638 = 7 + 77 + 777 + 7777.

8640 = 2! × 3! × 6!.

8641 is the number of ways to tile a 3×25 rectangle with 3×1 rectangles.

8642 has digits in

arithmetic sequence.
8646 divides 2

^{8646} + 2.

8649 is a value of n for which 2n and 7n together use each digit exactly once.

8657 is the number of ways to tile a 4×30 rectangle with 4×1 rectangles.

8658 is the sum of the first 4

perfect numbers.
8663 has the property that if each digit is replaced by its

square, the resulting number is a square.
8664 = 888 + 6666 + 666 + 444.

8666 has a 9

^{th} root whose decimal part starts with the digits 1-9 in some order.

8669 is the maximum value of n so
that there exist 5 denominations of stamps so that every postage from 1
to n can be paid for with at most 18 stamps.

8670 is a value of n for which n

!! - 1 is prime.
8672 is the number of

14-ominoes that tile the plane by translation.
8680 has a base 5 representation that ends with its base 7 representation.

8681 has a base 5 representation that ends with its base 7 representation.

8682 has a base 5 representation that ends with its base 7 representation.

8683 has a base 5 representation that ends with its base 7 representation.

8684 has a base 5 representation that ends with its base 7 representation.

8688 is the number of possible configurations of pegs (up to symmetry) after 26 jumps in solitaire.

8695 is a centered tetrahedral number.

8697 is a structured octagonal anti-diamond number.

8698 is a

strobogrammatic number.
8703 has a

cube that is the sum of 3 positive cubes.
8712 is 4 times its reverse.

8714 is the number of ways 24 people around a round table can shake hands in a non-crossing way, up to rotation.

8718 is the smallest n for which Σ

_{k≤n} 1/(k ln k) ≥ 3.

8721 is a value of n for which

φ(n) and σ(n) are square.
8732 has exactly the same digits in 3 different bases.

8736 is the smallest number that appears in its

factorial 10 times.
8739 is a permutation of the sum of its

proper divisors.
8743 is a number whose sum of

divisors is a 4^{th} power.
8744 is the number of subsets of {1,2,3,...,17} that have a sum divisible by 15.

8745 is the number of ways to divide a 13×13 grid of points into two sets using a straight line.

8748 is the largest number whose

prime factors add to 25.
8751 is a

perfect totient number.
8753 = 88 + 7777 + 555 + 333.

8758 = 88 + 7777 + 5 + 888.

8761 is the number of ordered

partitions of 25 into distinct parts.
8763 and its successor have the same digits in their

prime factorization.
8765 has digits in

arithmetic sequence.
8771 2

^{4} + 3

^{4} + 4

^{4} + 5

^{4} + 6

^{4} + 7

^{4} + 8

^{4}.

8772 is the sum of the first eight 4

^{th} powers.

8778 is both a

triangular number and 3 times a triangular number.
8779 is is the largest

prime factor of 100000000001.
8781 is the closest

integer to 18^{π}.
8784 is a value of n for which 2n and 5n together use each digit exactly once.

8785 is the number of

13-iamonds without holes.
8788 is an

Achilles number.
8793 is a value of n for which n

!!! - 1 is prime.
8796 is a value of n for which 5n and 7n together use each digit exactly once.

8797 is a structured hexagonal diamond number.

8801 is the magic constant of a 26×26 magic square.

8808 is the number of

partitions of 58 into distinct parts.
8810 has a

square whose digits each occur twice.
8813 is the number of

chiral invertible knots with 14 crossings.
8814 is the number of

multigraphs with 27 vertices and 4 edges.
8816 is a value of n for which reverse(

φ(n)) = φ(reverse(n)).
8819 is the smallest number whose

square begins with four 7's.
8820 is a highly abundant number.

8821 has the property that if each of its digits is replaced by its

cube, the result is a square.
8826 is the sum of its

proper divisors that contain the digit 4.
8829 is a value of n for which 6n and 7n together use each digit exactly once.

8830 is the number of lines passing through at least 2 points of an 14×14 grid of points.

8831 would be

prime if preceded and followed by a 1, 3, 7, or 9.
8833 = 88

^{2} + 33

^{2}.

8835 is the index of a

triangular number containing only 3 different digits.
8837 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with

integer dimensions less than 17.
8838 and its reverse are both the averages of

twin primes.
8840 is the number of triangles of any size contained in the triangle of side 32 on a triangular grid.

8843 is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with

integer dimensions less than 22.
8846 is the number of

divisors of the 20^{th} perfect number.
8854 is the number of possible rows in a 20×20 crossword puzzle.

8855 is a

Lucas-Carmichael number.
8856 is the number of subsets of {1,2,3,...,16} that have an

integer average.
8857 is a structured truncated tetrahedral number.

8860 is the smallest number n so that n+3, n

^{2}+3

^{2}, n

^{4}+3

^{4}, and n

^{8}+3

^{8} are all

prime.
8864 is a value of n for which |cos(n)| is smaller than any previous

integer.
8867 is the smallest

prime with multiplicative persistence 6.
8874 has a

square that is the concatenation of two consecutive even numbers.
8878 is the number of intersections when all the diagonals of a

regular 23-gon are drawn.
8883 does not occur in its

factorial in base 2.
8887 is a value of n for which

σ(n) is a repdigit.
8888 is a

repdigit.
8892 is a

betrothed number.
8902 is the number of possibilities for the first 1.5 moves in Chess.

8905 multiplied by its successor gives a number concatenated with itself.

8910 is divisible by its reverse.

8911 is a

Carmichael number.
8913 is the maximum value of n so
that there exist 4 denominations of stamps so that every postage from 1
to n can be paid for with at most 27 stamps.

8922 is the sum of its

proper divisors that contain the digit 4.
8923 is the numerator of 1 / 1

^{1} + 1 / 2

^{2} + 1 / 3

^{3} + 1 / 4

^{4}.

8925 is an odd

primitive abundant number.
8930 = 8888 + 9 + 33 + 0.

8931 = 8888 + 9 + 33 + 1.

8932 = 8888 + 9 + 33 + 2.

8933 = 8888 + 9 + 33 + 3.

8934 = 8888 + 9 + 33 + 4.

8935 = 8888 + 9 + 33 + 5.

8936 = 8888 + 9 + 33 + 6.

8937 = 8888 + 9 + 33 + 7.

8938 = 8888 + 9 + 33 + 8.

8939 = 8888 + 9 + 33 + 9.

8942 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8944 is the sum of the

cubes of the first 7 primes.
8950 has a 4

^{th} root whose decimal part starts with the digits 1-9 in some order.

8953 is the 10

^{th} central trinomial coefficient.
8954 is the first of four consecutive

squareful numbers.
8958 has a 4

^{th} power whose product of digits is also a 4

^{th} power.

8959 is the smallest multiple of 31 whose digits add to 31.

8964 is the smallest number with the property that its first 6 multiples contain the digit 8.

8965 is a value of n for which n

^{2} and n

^{3} use the same digits.

8968 is a

strobogrammatic number.
8970 = 8 + 9

^{4} + 7

^{4} + 0.

8971 = 8 + 9

^{4} + 7

^{4} + 1.

8972 = 8 + 9

^{4} + 7

^{4} + 2.

8973 = 8 + 9

^{4} + 7

^{4} + 3.

8974 = 8 + 9

^{4} + 7

^{4} + 4.

8975 = 8 + 9

^{4} + 7

^{4} + 5.

8976 = 8 + 9

^{4} + 7

^{4} + 6.

8977 = 8 + 9

^{4} + 7

^{4} + 7.

8978 = 8 + 9

^{4} + 7

^{4} + 8.

8979 = 8 + 9

^{4} + 7

^{4} + 9.

8980 is a value of n for which the first n binary digits of

π form a prime.
8982 uses the same digits as

φ(8982).
8989 is a

Delannoy number.
8991 is the smallest number so that it and its successor are both the product of a

prime and the 5^{th} power of a prime.
8993 is a

Huay rhombic dodecahedral number.
8999 is the smallest number whose digits add to 35.

9000 is the index of a

triangular number containing only 3 different digits.
9002 is a value of n so that n(n+7) is a

palindrome.
9005 is the number of inequivalent

Ferrers graphs with 36 points.
9006 is a

strobogrammatic number.
9009 is a

centered cube number.
9011 has a

square that is the concatenation of two consecutive odd numbers.
9012 is the sum of its

proper divisors that contain the digit 5.
9016 is the number of

perfect squared rectangles of order 16.
9018 has a

square with the last 3 digits the same as the 3 digits before that.
9020 is the number of ways to color the vertices of a triangle with 30 colors, up to rotation.

9023 has the property that the concatenation of its

prime factors in increasing order is a square.
9024 is the number of regions formed when all diagonals are drawn in a

regular 24-gon.
9025 is a

Friedman number.
9028 is the number of ways to tile a 9×4 rectangle with

integer-sided squares.
9032 would be

prime if preceded and followed by a 1, 3, 7, or 9.
9036 has a 9

^{th} power that contains the same digits as 3585

^{10}.

9037 is a value of n for which 2n and 7n together use each digit exactly once.

9038 is the number of

conjugacy classes of the alternating group A_{36}.
9042 is the

trinomial coefficient T(11,4).
9045 is the number of ways to 18-color the faces of a

tetrahedron.
9048 is the number of regions the

complex plane is cut into by drawing lines between all pairs of 24^{th} roots of unity.
9049 is an Eisenstein-Mersenne prime.

9052 is the maximum number of regions space can be divided into by 31

spheres.
9055 is the index of a

triangular number containing only 3 different digits.
9056 is a cubic star number.

9059 has an 8

^{th} root that starts 3.12345....

9070 has a 4

^{th} root whose decimal part starts with the digits 1-9 in some order.

9072 has a base 2 and base 3 representation that end with its base 6 representation.

9073 has a base 2 and base 3 representation that end with its base 6 representation.

9074 has a base 3 representation that ends with its base 6 representation.

9077 is a

Markov number.
9078 has a

cube whose digits occur with the same frequency.
9079 has a

square that is the concatenation of two consecutive decreasing numbers.
9086 is the number of regions formed when all diagonals are drawn in a

regular 23-gon.
9091 is the only

prime known whose reciprocal has period 10.
9093 has a

square with the first 3 digits the same as the next 3 digits.
9099 is the number of ways to 3-color the faces of a

dodecahedron.
9101 has a

square where the first 6 digits alternate.
9104 has a

square with the first 3 digits the same as the next 3 digits.
9105 is the number of possible positions in Checkers after 6 moves.

9108 is a

heptagonal pyramidal number.
9109 is the number of regions the

complex plane is cut into by drawing lines between all pairs of 23^{rd} roots of unity.
9113 is a

narcissistic number in base 5.
9115 has a base 3 representation that begins with its base 6 representation.

9116 is a

strobogrammatic number.
9117 is a value of n for which 6n and 7n together use each digit exactly once.

9119 is the number of symmetric

plane partitions of 34.
9121 is the number of possibilities for the last 5 digits of a

square.
9126 is a

pentagonal pyramidal number.
9134 has a 10

^{th} root whose decimal part starts with the digits 1-9 in some order.

9135 is a value of n for which 2n and 7n together use each digit exactly once.

9137 has a 4

^{th} power that is the sum of four 4

^{th} powers.

9138 is the number of

13-iamonds without bilateral symmetry.
9139 =

_{39}C_{3}.
9152 and its successor are both divisible by 4

^{th} powers.

9153 is a value of n for which 2n and 3n together use each digit exactly once.

9154 is a value of n for which

φ(n) and σ(n) are square.
9156 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9158 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9162 is a value of n for which 5n and 8n together use each digit exactly once.

9168 = 27504 / 3, and each digit is contained in the equation exactly once.

9172 is the number of connected planar maps with 7 edges.

9174 is the sum of its

proper divisors that contain the digit 5.
9176 is the maximum number of pieces a

torus can be cut into with 37 cuts.
9178 is the maximum number of regions a

cube can be cut into with 38 cuts.
9179 is a value of n for which

φ(n) = φ(n-1) + φ(n-2).
9182 is a value of n for which 4n and 5n together use each digit exactly once.

9183 is the number of sets of distinct positive

integers with mean 8.
9185 is a value of n for which 2n and 7n together use each digit exactly once.

9189 is the number of sided

10-ominoes.
9191 is not the sum of a

square, a cube, a 4^{th} power, and a 5^{th} power.
9196 has the property that dropping its first and last digits gives its largest

prime factor.
9198 is the number of

ternary square-free words of length 25.
9201 is a

truncated octahedral number.
9214 is the number of ways to stack 30 pennies in contiguous rows so that each penny lies on the table or on two pennies.

9216 is a

Friedman number.
9217 is the total number of digits of all

binary numbers of length 1-10.
9219 is a value of n for which |cos(n)| is smaller than any previous

integer.
9224 is an

octahedral number.
9233 is the number of different arrangements (up to rotation and reflection) of 13 non-attacking

queens on a 13×13 chessboard.
9234 is the number of

multigraphs with 7 vertices and 10 edges.
9235 is the number of

13-iamonds.
9237 is a value of n for which n and 5n together use each digit 1-9 exactly once.

9240 =

_{22}P_{3}.
9241 is a

Cuban prime.
9243 has a 4

^{th} power that is the sum of four 4

^{th} powers.

9248 is the number of possible rook moves on a 17×17 chessboard.

9250 = (10

^{3} + 10

^{4} + 10

^{5} + 10

^{6}) / (3 × 4 × 5 × 6).

9251 has a

square whose digits each occur twice.
9252 is the number of necklaces with 10 white and 10 black beads.

9253 is the smallest number that appears in its

factorial 9 times.
9261 is a

Friedman number.
9267 is a value of n for which n and 2n together use each digit 1-9 exactly once.

9268 is a value of n for which 2

φ(n) = φ(n+1).
9272 is a

weird number.
9273 is a value of n for which n and 2n together use each digit 1-9 exactly once.

9282 is the product of three consecutive

Fibonacci numbers.
9284 is the number of ways to place 2 non-attacking

bishops on a 12×12 chessboard.
9285 is the number of

16-hexes with reflectional symmetry.
9286 is a

narcissistic number in base 7.
9287 is the number of stretched

10-ominoes.
9288 can be written as the sum of 2, 3, 4, or 5 positive

cubes.
9289 is a

Tetranacci-like number starting from 1, 1, 1, and 1.
9296 is the number of ways to break {1,2,3, . . . ,17} into sets with equal sums.

9298 has the property that the concatenation of its

prime factors in increasing order is a square.
9304 = 65128 / 7, and each digit is contained in the equation exactly once.

9305 has the property that if each digit is replaced by its

square, the resulting number is a square.
9306 is a value of n for which 3n and 5n together use each digit exactly once.

9310 is a decagonal pyramidal number.

9311 is the index of a

prime Fibonacci number.
9313, when followed by any of its digits, is

prime.
9314 is the 13

^{th} Iccanobif number.

9315 is a value of n for which 2n and 3n together use each digit exactly once.

9316 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9321 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9324 is the

reciprocal of the sum of the reciprocals of 14652 and its reverse.
9327 is a value of n for which n and 2n together use each digit 1-9 exactly once.

9330 is the

Stirling number of the second kind S(10,3).
9331 has the property that the sum of its

prime factors is equal to the product of its digits.
9339 is a value of n for which

φ(n) = φ(n-2) - φ(n-1).
9347 is a value of n for which the sum of

square-free divisors of n and n+1 are the same.
9348 has a 8

^{th} power that contains the same digits as 3588

^{9}.

9349 is the 19

^{th} Lucas number.
9350 appears inside its 4

^{th} power.

9352 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9360 is a value of n for which

σ(n-1) = σ(n+1).
9362 = 22222 in base 8.

9363 is the number of tilted rectangles with vertices in a 15×15 grid.

9364 is the number of

connected digraphs with 5 vertices.
9367 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.
9371 is a

prime that remains prime when preceded and followed by one, two, three, or four 3's.
9374 is a value of n for which

φ(σ(n)) = φ(n).
9375 has a

cube that ends with those digits.
9376 is an

automorphic number.
9377 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in

Roman numerals.
9378 is a value of n for which 4n and 5n together use each digit exactly once.

9380 is the number of lines through exactly 2 points of a 15×15 grid of points.

9382 is a value of n for which 4n and 5n together use each digit exactly once.

9383 is the index of a

Fibonacci number whose first 9 digits are the digits 1-9 rearranged.
9385 is the sum of consecutive

squares in 2 ways.
9386 = 99 + 333 + 8888 + 66.

9387 is a

Smith brother.
9391 has a

square with the first 3 digits the same as the last 3 digits.
9393 is the number of non-

isomorphic 3×3×3 Rubik's cube positions that require exactly 5 quarter turns to solve.
9394 is a value of n so that n(n+8) is a

palindrome.
9396 is the number of

symmetric 3×3 matrices in base 6 with determinant 0.
9403 = 65821 / 7, and each digit is contained in the equation exactly once.

9406 is the index of a

triangular number containing only 3 different digits.
9407 has a 7

^{th} root whose decimal part starts with the digits 1-9 in some order.

9408 is the number of reduced 6×6

Latin squares.
9413 has a

cube whose digits occur with the same frequency.
9415 is the sum of the first 19 numbers that have digit sum 19.

9416 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9421 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9424 has the property that the fractional part of

π^{9424} begins .9424....
9426 is a value of n for which 5n and 7n together use each digit exactly once.

9427 is the smallest number that can not be formed using the digit 1 at most 29 times, together with the symbols +, –, × and ÷.

9428 is the smallest number whose

square begins with four 8's.
9431 is a number n for which n, n+2, n+6, and n+8 are all

prime.
9432 is the number of 3-colored

rooted trees with 6 vertices.
9436 is the smallest number whose 15

^{th} power contains exactly the same digits as another 15

^{th} power.

9439 is

prime, and 5 closest primes are all smaller.
9444 has a

square with the first 3 digits the same as the next 3 digits.
9445 is the closest

integer to 29^{e}.
9450 is the denominator of

ζ(8) / π^{8}.
9451 is the number of

binary rooted trees with 19 vertices.
9452 is the smallest number whose

cube contains 5 consecutive 4's.
9455 is the sum of the first 30

squares.
9465 is an hexagonal prism number.

9468 is the sum of its

proper divisors that contain the digit 7.
9471 is an octagonal pyramidal number.

9473 is a

Proth prime.
9474 is a

narcissistic number.
9477 is the maximum

determinant of a binary 13×13 matrix.
9481 is a number whose sum of

divisors is a 4^{th} power.
9489 is the closest

integer to π^{8}.
9493 is a member of the

Fibonacci-type sequence starting with 1 and 9.
9496 is the number of 10×10

symmetric permutation matrices.
9497 is the number of

bicentered trees with 16 vertices.
9499 has a 5

^{th} power whose first few digits are 77337377....

9500 is a

hexagonal pyramidal number.
9504 is a

betrothed number.
9513 is the smallest number
without increasing digits that is divisible by the number formed by
writing its digits in increasing order.

9519 has a 4

^{th} power that is the sum of four 4

^{th} powers.

9520 is an enneagonal pyramidal number.

9523 is a value of n for which 4n and 5n together use each digit exactly once.

9529 is the number of 3×3 sliding puzzle positions that require exactly 18 moves to solve starting with the hole in a corner.

9531 is the index of a

prime Woodall number.
9538 is a value of n for which 4n and 5n together use each digit exactly once.

9541 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9542 is the number of ways to place a non-attacking white and black pawn on a 11×11 chessboard.

9545 is a number with the property that the

root-mean-square of its divisors is an integer.
9551 has the same digits as the 9551

^{st} prime.
9552 and the following 34 numbers are

composite.
9555 is an odd

primitive abundant number.
9563 = 9 + 5555 + 666 + 3333.

9564 is the number of paraffins with 10 carbon atoms.

9568 = 9 + 5 + 666 + 8888.

9574 is a value of n for which |cos(n)| is smaller than any previous

integer.
9576 = 19

!!!!!.
9583 is the number of subsets of {1, 2, 3, ... 20} that do not contain solutions to x + y = z.

9592 is the number of

primes with 5 or fewer digits.
9596 is the index of a

triangular number containing only 3 different digits.
9601 is a

Proth prime.
9602 has the property that if each digit is replaced by its

square, the resulting number is a square.
9605, when concatenated with 4 less than itself, is

square.
9608 is the number of

digraphs with 5 vertices.
9615 is the smallest number whose

cube starts with 5 identical digits.
9616 is an icosahedral number.

9623 is the number of symmetric 10-cubes.

9625 has a

square formed by inserting a block of digits inside itself.
9627 is a value of n for which n and 5n together use each digit 1-9 exactly once.

9629 is a value of n for which 2n and 7n together use each digit exactly once.

9632 is the number of different arrangements of 4 non-attacking

queens on a 4×14 chessboard.
9633 is a

Smith brother.
9634 is a

Smith brother.
9639 has a 4

^{th} power that is the sum of four 4

^{th} powers.

9643 is the smallest number that can not be formed using the numbers 2

^{0}, 2

^{1}, ... , 2

^{7}, together with the symbols +, –, × and ÷.

9648 is a factor of the sum of the digits of 9648

^{9648}.

9653 = 99 + 666 + 5555 + 3333.

9658 = 99 + 666 + 5 + 8888.

9660 is a

truncated tetrahedral number.
9670 is the number of 8-digit

triangular numbers.
9673 is the number of triangles of any size contained in the triangle of side 33 on a triangular grid.

9677 is a

prime that remains prime if any digit is deleted.
9682 is a value of n for which n

!! - 1 is prime.
9689 is the exponent of a

Mersenne prime.
9691 has the property that the concatenation of its

prime factors in increasing order is a square.
9695 is the sum of the digits of 5

^{55}.

9696 is a

strobogrammatic number.
9700 is the number of inequivalent 4-digit strings, where two strings are equivalent if turning one upside down gives the other.

9701 has a

square whose digits each occur twice.
9707 does not occur in its

factorial in base 2.
9709 has a

cube whose digits occur with the same frequency.
9711 uses the same digits as

π(9711).
9716 is the number of Pyramorphix puzzle positions that require exactly 5 moves to solve.

9720 is the order of a

perfect group.
9721 is the largest

prime factor of 1234567.
9723 is a value of n for which n and 5n together use each digit 1-9 exactly once.

9724 = 1111 in base 21.

9726 is the smallest number in base 5 whose

square contains the same digits in the same proportion.
9728 can be written as the sum of 2, 3, 4, or 5 positive

cubes.
9738 is the number of

trees on 22 vertices with diameter 5.
9747 is an

Achilles number.
9748 is the maximum value of n so
that there exist 6 denominations of stamps so that every postage from 1
to n can be paid for with at most 14 stamps.

9751 is the number of possible configurations of pegs (up to symmetry) after 8 jumps in solitaire.

9753 is a value of n for which 4n and 5n together use each digit exactly once.

9754 is the number of paths between opposite corners of a 3×5 rectangle

graph.
9760 can be written as the product of a number and its reverse in 2 different ways.

9764 would be

prime if preceded and followed by a 1, 3, 7, or 9.
9765 is an odd

primitive abundant number.
9767 is the largest 4 digit

prime composed of concatenating two 2 digit primes.
9768 = 2 × 22 × 222.

9770 is the number of

Hamiltonian cycles of a 4×12 rectangle graph.
9775 is a number n so that the sum of the digits of n

^{n}-1 is divisible by n.

9777 is the number of

graphs on 8 vertices with no isolated vertices.
9779 has a

square root that has four 8's immediately after the decimal point.
9784 is the number of 2 state

Turing machines which halt.
9786 has a

square whose digits each occur twice.
9789 is the smallest number that appears in its

factorial 11 times.
9790 is the number of ways to place 2 non-attacking kings on a 12×12 chessboard.

9792 is the number of

partitions of 59 into distinct parts.
9793 is the smallest number that can be written as the sum of 4 distinct positive

cubes in 5 ways.
9796 has the property that dropping its first and last digits gives its largest

prime factor.
9797 is the product of two consecutive

primes.
9798 is a number whose sum of

divisors is a 4^{th} power.
9799 is a number with the property that the

root-mean-square of its divisors is an integer.
9800 is the largest 4-digit number with single digit

prime factors.
9801 is 9 times its reverse.

9802, when concatenated with one less than it, is

square.
9803 is the number of different

degree sequences possible for a graph with 19 edges.
9805 is the number of subsequences of {1,2,3,...15} in which every odd number has an even neighbor.

9809 is a

stella octangula number.
9823 is the number of

centered trees with 16 vertices.
9824 is a structured snub cubic number.

9828 is the order of a

non-cyclic simple group.
9831 has a base 6 representation which is the reverse of its base 5 representation.

9839 would be

prime if preceded and followed by a 1, 3, 7, or 9.
9841 = 111111111 in base 3.

9843 is the number of vertices in a

Sierpinski triangle of order 8.
9849 is a centered tetrahedral number.

9854 is the index of a

triangular number containing only 3 different digits.
9855 is a

rhombic dodecahedral number.
9856 is the number of ways to place 2 non-attacking

knights on a 12×12 chessboard.
9857 is a

Proth prime.
9858 is a number whose sum of

divisors is a 4^{th} power.
9861 is a dodecagonal pyramidal number.

9862 is the number of

knight's tours on a 6×6 chessboard.
9865 is the number of digits in the 15

^{th} Fermat number.
9868 is the number of hydrocarbons with 10 carbon atoms.

9871 is the largest 4-digit

prime with different digits.
9872 = 8 + 88 + 888 + 8888.

9876 is the largest 4-digit number with different digits.

9877 has a 4

^{th} power that is the sum of four 4

^{th} powers.

9878 has a 10

^{th} power whose first few digits are 88448448....

9880 =

_{40}C_{3}.
9886 is a

strobogrammatic number.
9888 is the number of

connected graphs with 8 vertices whose complements are also connected.
9894 is the number of 3-colored

trees with 7 vertices.
9896 is the number of Pyraminx puzzle positions that require exactly 6 moves to solve.

9900 = 10011010101100

_{2} = 9900

_{10} = 1881

_{19} = 1199

_{21}, each using two digits the same number of times.

9901 is the only

prime known whose reciprocal has period 12.
9910 is the number of fixed

9-ominoes.
9911 has the property that the sum of its

prime factors is equal to the product of its digits.
9912 is the number of

graceful permutations of length 14.
9913, when followed by any of its digits, is

prime.
9918 is the maximum number of pieces a

torus can be cut into with 38 cuts.
9919 can be written as the difference between two positive

cubes in more than one way.
9920 is the maximum number of regions a

cube can be cut into with 39 cuts.
9928 is a value of n for which reverse(

φ(n)) = φ(reverse(n)).
9929 is the number of 3×3 sliding puzzle positions that require exactly 26 moves to solve starting with the hole on a side.

9933 = 441 + 442 + . . . + 462 = 463 + 464 + . . . + 483.

9941 is the exponent of a

Mersenne prime.
9944 = 10011011011000

_{2} = 9944

_{10} = 2E2E

_{15} = 11BB

_{21}, each using two digits the same number of times.

9945 = 17

!!!!.
9951 is the number of ways to color the vertices of a triangle with 31 colors, up to rotation.

9959 is a member of the

Fibonacci-type sequence starting with 2 and 5.
9960 is the number of 3×3×3 sliding puzzle positions that require exactly 8 moves to solve.

9966 is the largest 4-digit

strobogrammatic number.
9973 is the largest 4-digit

prime.
9976 has a

square formed by inserting a block of digits inside itself.
9984 is the maximum number of regions space can be divided into by 32

spheres.
9985 is the number of

hyperbolic knots with 13 crossings.
9988 is the number of

prime knots with 13 crossings.
9992 is the number of 2×2×2

Rubik's cube positions that require exactly 5 moves to solve.
9995 has a

square formed by inserting a block of digits inside itself.
9996 has a

square formed by inserting a block of digits inside itself.
9998 is the smallest number n for which the concatenation of n, (n+1), ... (n+21) is

prime.
9999 is a

Kaprekar number.
Source :

http://www2.stetson.edu/~efriedma/numbers.html