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Annotated version of "What's Special About This Number?" (Part 0)
From OeisWiki
Introduction
Erich Friedman has a very nice (and deservedly popular) page called What's Special About This Number?
It does not, however, mention the sequences in the OEIS where these numbers can be found (and from where I suspect most of the entries were taken).
The present set of ten pages is a snapshot of his page as of May 23, 2010, with pointers to the corresponding entries in the OEIS. The pages are:
- Part 0: 0 to 999,
- Part 1: 1000 to 1999,
- Part 2: 2000 to 2999,
- Part 3: 3000 to 3999,
- Part 4: 4000 to 4999,
- Part 5: 5000 to 5999,
- Part 6: 6000 to 6999,
- Part 7: 7000 to 7999,
- Part 8: 8000 to 8999,
- Part 9: 9000 to 9999.
People are invited to add more pointers to these pages, by adding the appropriate A-numbers to the entries. It may be necessary to create new sequences to do this - see A158304 for an example.
To add a link to sequence A000108, for example, type A000108.
I should add that this is being done with Erich Friedman's approval.
I did not do a very good job of converting the original html format to wiki format, and in some cases you may have to refer to Erich's page to figure out the meaning or the links.
You may well find better descriptions for some numbers. If so, please send them to Erich and make the corresponding changes here. (The wiki software is complaining that these pages are too long. I decided to ignore these complaints.)
Neil Sloane
Part 0: The Numbers 0 to 999
0 is the additive identity (A000004)
1 is the multiplicative identity (A000012)
2 is the only even prime (A000040). It is also the largest integer which satisfies x+x = x*x = x^{x}
3 is the number of spatial dimensions we live in
4 is the smallest number of colors sufficient to color all planar maps (A000934, A158411)
5 is the number of Platonic solids
6 is the smallest perfect number (A000396)
7 is the smallest number of sides of a regular polygon that is not constructable by straight-edge and compass (A003401, A004169)
8 is the largest cube in the Fibonacci sequence (A000045, A000578)
9 is the maximum number of cubes that are needed to sum to any positive integer (A002376)
10 is the base of our number system
11 is the largest known multiplicative persistence (A003001, A031346)
12 is the smallest abundant number (A005101)
13 is the number of Archimedian solids
14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers (A005277)
15 is the smallest composite number n with the property that there is only one group of order n (A000001, A050384)
16 is the only number of the form x^{y} = y^{x} with x and y different integers
17 is the number of wallpaper groups
18 is the only number (other than 0) that is twice the sum of its digits (A169805, A007953)
19 is the maximum number of 4^{th} powers needed to sum to any number (A002377)
20 is the number of rooted trees with 6 vertices (A000081)
21 is the smallest number of distinct squares needed to tile a square (A006983)
22 is the number of partitions of 8 (A000041)
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 (nonzero) squares (A134422)
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 (A000396)
29 is the 7^{th} Lucas number (A000032)
30 is the largest number with the property that all smaller numbers relatively prime to it are prime
31 is a Mersenne prime (A000043, A000668)
32 is the smallest non-trivial 5^{th} power (A000584)
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 (A169834, A005238)
35 is the number of hexominoes (A000105)
36 is the smallest non-trivial number which is both square (A000290) and triangular (A000217) (I.e. is in A001110)
37 is the maximum number of 5^{th} powers needed to sum to any number. It is also the third (and probably the last) prime of the form 4k+1, for which all sums Sum_{j=1..u} L(j/p) (with u ranging from 1 to (p-1)/2) are nonnegative, where L(j/p) is Legendre symbol of j and p. (A080114)
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, and the last one which is an integral multiple of the immediately preceding Catalan number (C_{4} = 14). (A000108)
43 is the number of sided 7-iamonds
44 is the number of derangements of 5 items (A000166)
45 is a Kaprekar number (A006886)
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 (A000110)
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 (A000217) in the Fibonacci sequence (A000045). It is the tenth term (after the zero) in both sequences, 55 = A000217(10) = A000045(10)
56 is the number of reduced 5×5 Latin squares A000315)
57 = 111 in base 7 (A023000)
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 (A169823).
60 is also the order of the smallest non-cyclic simple group (A001034)
61 is the 3^{rd} secant number (A000364)
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 on 5 elements (A000112)
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 has the property that 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 (A001116)
73 is the smallest multi-digit number which is one less than twice its reverse (A169830)
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 (A000670)
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 the only number known whose square has no isolated digits
89 = 8^{1} + 9^{2} (A028387)
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 (A006886)
100 is the smallest square which is also the sum of 4 consecutive non-zero cubes A027603 (Are there others?)
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 (A000043, A000668)
108 is 3 hyperfactorial
108 is also the number of heptominoes (A000105)
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 (A125725)
115 is the number of rooted trees with 8 vertices (A000081)
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. It is also the third (and probably the last?) number which is both factorial (A000142) and triangular number (A000217)
121 is the only square known of the form 1 + p + p^{2} + p^{3} + p^{4}, where p is prime
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 (A000032)
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 = [1] binomial(9,4) (A007318)
127 is a Mersenne prime (A000043, A000668)
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 (A000290) in the Fibonacci sequence (A000045). It is the twelfth term (after the zero) in both sequences, 144 = A000290(12) = A000045(12)
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 (A002385)
152 has a square composed of the digits 0-4 (A158304)
153 is a narcissistic number (A005188)
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 (A169802, A055233)
156 is the number of graphs with 6 vertices (A000088)
157 is a number whose square contains the same digits as the square of its successor (A072841 (the defintion was wrong)
158 is the number of planar partitions of 11 (A000219)
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 (A001034)
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 distinct 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 (A000032)
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 (A000110)
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} (A000032)
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 (A000225)
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 (A001116)
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 (A000081)
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 (A006886)
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 (A060853)
301 is a 6-hyperperfect number
302 is the number of ways to play the first 3 moves in checkers (A133046)
303 is the number of bipartite graphs with 8 vertices
304 is a primitive semiperfect number
305 is a hexagonal prism number (A005915)
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 a value of n for which one less than the product of the first n primes is prime
318 is the number of unlabeled partially ordered sets on 6 elements (A000112)
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 X 10 matrix
321 is a Delannoy number
322 is the 12^{th} Lucas number (A000032)
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.
360 is also the order of a non-cyclic simple group (A001034)
361 is the number of intersections on a Go board (A000290)
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 (A000105)
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 (A000045)
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
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 (A006972)
400 = 1111 in base 7 (A023000)
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 (A169825)
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 (A000396)
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 (A000225)
512 is the cube of the sum of its digits
513 is the number of conjugacy classes of the alternating group A_{22}
514 ???
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 (A000032)
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 (A092336)
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 (A169824)
541 is the number of orderings of 5 objects with ties allowed (A000670)
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 (A000043, A000668)
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 ???
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 (A066408)
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 (A006886)
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 (A000081)
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 a pentagonal pyramidal number
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 (A061193)
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 (A125725)
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 2φ (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 ???
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 (A000032)
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 (A066538)
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 (A001349)
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 (A000219)
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 (A000009)
865 ???
866 is the number of sided 10-iamonds (A006534)
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 (A048211)
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 (A002981)
873 = 1! + 2! + 3! + 4! + 5! + 6! (A007489)
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 (A007587)
877 is the 7^{th} Bell number (A000110)
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 (A006052)
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 (A007584)
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 (A003261)
896 is not the sum of 4 non-zero squares
897 is a Cullen number (A002064)
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 (A006972)
936 is a pentagonal pyramidal number
937 ???
938 ???
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 (A005101, A005231)
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 (A093112)
960 is the sum of its digits and the cube of its digits (A065138)
961 is a square whose digits can be rotated to give another square (A035126)
962 ???
963 is a value of n for which π(n) is the product of the digits of n (A097220)
964 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in the center (A089474)
965 ???
966 is the Stirling number of the second kind S(8,3) (A008277, A048993, A000392)
967 is the number of 6-digit triangular numbers (A068094)
968 is an Achilles number (A052486)
969 is a tetrahedral palindrome (A006030)
970 ???
971 ???
972 is an Achilles number (A052486)
973 is the number of inequivalent asymmetric Ferrers graphs with 25 points (A000701)
974 is the number of multigraphs with 5 vertices and 10 edges (A014395)
975 is the number of 11-ominoes that contain 1 hole (A057418)
976 has a square formed by inserting a block of digits inside itself (A052212)
977 is a Stern prime (A042978)
978 2^{4} + 3^{4} + 4^{4} + 5^{4}
979 is the sum of the first five 4^{th} powers (A000538)
980 ???
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 (A000009)
983 is a Wedderburn-Etherington number (A001190)
984 = 8 + 88 + 888 (A099675)
985 is the 9^{th} Pell number (A000129)
986 is a strobogrammatic number (A000787)
987 is the 16^{th} Fibonacci number (A000045)
988 is the maximum number of regions a cube can be cut into with 18 cuts (A000125)
989 is the smallest number such that it and its reverse are divisible by 43 (A055483)
990 is a triangular number that is the product of 3 consecutive integers (A001219)
991 is a permutable prime (A003459, A129338)
992 is the number of differential structures on the 11-dimensional hypersphere (A001676)
993 is the number of paraffins with 8 carbon atoms (A005961)
994 is the smallest number with the property that its first 18 multiples contain the digit 9 (A039940)
995 has a square formed by inserting a block of digits inside itself (A046829)
996 has a square formed by inserting a block of digits inside itself (A046829)
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 (A039940)
999 is a Kaprekar number (A006886)