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Annotated version of "What's Special About This Number?" (Part 3)
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.
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
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 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
3245 in hexadecimal spells the word CAD
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
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
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