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## Introduction

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:

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.

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 3: The Numbers 3000 to 3999

3000 is the number of symmetric arrangements of 7 non-attacking queens on a 7×7 chessboard

3001 is 1/24 of the 24th Fibonacci number (A000045)

3003 is the only number known to appear 8 times in Pascal's triangle

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 (A000041)

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 = 9P 4

3025 is the sum of the first 10 cubes

3028 are the first 4 digits of 53028

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

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

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 = 18C 4

3063 is a perfect totient number

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

3074 is the number of binary partitions of 37

3077 is the rectilinear crossing number of complete graph K23

3078 is a pentagonal pyramidal number

3080 is the number of drawings of the complete graph K9 with a minimal number of [http://3084 is the number of 3×3 sliding puzzle positions that require exactly 15 moves to solve starting with the hole in the center

3081 is a doubly triangular numbers

3087 is an 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 = 22C 3 + 22C 1 + 22C 0 + 22C 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 16th and the 17th Mersenne prime (A066538)

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

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 = 31215 + 31217 + 31218

3122 is the number of ordered sequences of coins totaling 29 cents

3124 = 44444 in base 5

3125 is a strong Friedman number

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 9th central trinomial coefficient

3141 is the integer part of 1000 π

3146 is a structured deltoidal hexacontahedral number

3148 has a square with the first 3 digits the same as the next 3 digits

3150 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

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 2nC n is not divisible by the first 5 primes

3161 is the smallest number whose square begins with three 9's

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

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 2nC 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

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

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

3210 is the smallest 4-digit number with decreasing digits

3212 = 37 + 29 + 17 + 29

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 (A000043, A000668)

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 C12H24 without any double bonds

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

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 2nC 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

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

3267 = 12345 in base 7

3274 = 3030224 = 1010445, each using 3 different digits exactly twice

3276 = 28C 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

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

3297 is a value of n for which 5n and 7n together use each digit exactly once

3300 is the number of non-isomorphic " groupoids on 4 elements

3301 is a value of n for which the nth 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

3311 is the sum of the first 21 squares

3312 = 332 + 122

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

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

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 = 16P 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 n2+1 is double another square

3366 = (19 + 29 + 39) / (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 23rd Mersenne prime (A028335)

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 2φ (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 = 33 + 44 + 55

3410 is a truncated square pyramid number

3411 is the number of inequivalent asymmetric Ferrers graphs with 31 points

3412 = 22 + 33 + 44 + 55

3413 = 11 + 22 + 33 + 44 + 55

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 7th central binomial coefficient

3433 is a narcissistic number in base 6

3435 = 33 + 44 + 33 + 55

3439 is a rhombic dodecahedral number

3440 is the closest integer to 20e

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 A31

3456 has digits in arithmetic sequence

3457 is a Proth prime

3459 has a 6th root that starts 3.88888...

3461 is a number n for which n, n+2, n+6, and n+8 are all prime

3465 = 15!!!!

3468 = 682 - 342

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

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 5th 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 5th 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 .

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)

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

3563 is a house number

3564 divides 11 + 22 + 33 + . . . + 35643564

3570 is both a triangular number and 6 times a triangular number

3571 is the 17th Lucas number

3577 is a Kaprekar constant in base 2

3579 has digits in arithmetic sequence

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 10th power that contains the same digits as 90369

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 4th powers

3594 is the smallest number whose 9th 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 (A060793)

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 3623th 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

3630 appears inside its 4th 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

3654 = 29C 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

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

3691 is a number n for which n2+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 K24