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# Annotated version of "What's Special About This Number?" (Part 7)

## 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 7: The Numbers 7000 to 7999

**7000** has a sum of digits equal to its largest prime factor (A052021)

**7001** is the number of 13-hexes that tile the plane by translation

**7002** is the number of arrangements of 4 non-attacking queens on a 8×8 chessboard

**7003** is the number of graphs with 9 vertices that have 8 automorphisms

**7014** has a square with the last 3 digits the same as the 3 digits before that

**7015** has a cube root whose decimal part starts with the digits 1-9 in some order

**7019** is a prime that remains prime if any digit is deleted (A051362)

**7028** is the smallest multi-digit number n, when written in base 17, gives a divisor of n

**7030** is an octagonal pyramidal number (A002414)

**7032** is the number of ternary square-free words of length 24

**7039** = 28156 / 4, and each digit is contained in the equation exactly once

**7040** has a sum of digits equal to its largest prime factor

**7055** is a Lucas-Carmichael number (A006972)

**7056** is a square that is the product of two triangular numbers (A169835, A169836)

**7057** is a Cuban prime (A007645)

**7060** has the property that the sum of the squares of its divisors ends with the digits 7060

**7066** is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 13 stamps (A001211)

**7068** is the number of series-reduced planted trees with 11 leaves (A000669)

**7071** is the smallest number whose square contains 4 consecutive 9's

**7072** is the generalized Catalan number C(10,7)

**7073** is a Leyland number

**7075** is the number of ways to stack 35 boxes in a line so that each box lies on the table or on a box next to 2 boxes

**7084** is the generalized Catalan number C(19,4)

**7089** is a value of n for which |cos(n)| is smaller than any previous integer

**7092** is the number of possible positions in Othello after 3 moves by both players

**7093** has a 6^{th} root that starts 4.38333833...

**7094** is the number of ways to place 34 points on a 17×17 grid so that no 3 points are on a line

**7096** is the number of 8-digit perfect powers

**7098** is the trinomial coefficient T(14,9) (A000574)

**7101** has a 4^{th} power that is the sum of four 4^{th} powers

**7102** is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged

**7106** is an octahedral number

**7107** has a square whose digits each occur twice

**7108** is the number of partitions of 56 into distinct parts

**7117** is a number whose sum of divisors is a 5^{th} power

**7119** has the same digits as the 7119^{th} prime

**7120** is the number of 2×2 singular matrices mod 10

**7122** = 7^{2} + 8^{3} + 9^{4}

**7123** is the number of 2-connected graphs with 8 vertices

**7140** is the largest number which is both triangular and tetrahedral

**7142** is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with integer dimensions less than 20

**7143** is 7-automorphic

**7145** has a square with the first 3 digits the same as the next 3 digits

**7150** has a sum of digits equal to its largest prime factor

**7152** has a square with the first 3 digits the same as the next 3 digits

**7159** has a square with the first 3 digits the same as the next 3 digits

**7161** is a Kaprekar constant in base 2

**7164** is a value of n for which n^{8}, n^{9}, n^{10}, and n^{11} have the same digit sum

**7170** is a value of n for which σ (n-1) = σ (n+1)

**7172** is a Kaprekar number for cubes

**7174** is the maximum number of pieces a torus can be cut into with 34 cuts

**7175** is a centered octahedral number

**7176** is the maximum number of regions a cube can be cut into with 35 cuts

**7187** is the smallest number that can not be formed using the digits 0-8 at most once, together with the symbols +, –, × and ÷

**7188** is the number of ways to permute 5 red, 5 white, and 5 blue balls

**7189** is the number of ways to color the vertices of a square with 13 colors, up to rotation

**7192** is a weird number

**7193** is a right-truncatable prime

**7197** is the smallest number whose 7^{th} power has 27 digits

**7200** is the order of a perfect group

**7201** is the number of 2×2 singular matrices mod 19

**7209** has a 4^{th} power that is the sum of four 4^{th} powers

**7212** is the number of unordered ways to write 1 as a sum of reciprocals of integers no larger than 20

**7225** is the number of ways to 17-color the faces of a tetrahedron

**7226** has a cube root that starts 19.3330030330...

**7230** is the sum of consecutive squares in 2 ways

**7235** is a value of n for which 4n and 5n together use each digit exactly once

**7236** uses the same digits as φ (7236)

**7240** = 1111 in base 19

**7241** is the number of asymmetric trees with 19 vertices

**7245** appears inside its 4^{th} power

**7248** is the number of lines through exactly 2 points of a 14×14 grid of points

**7253** has a square that remains square when a 6 is appended to it

**7254** = 186 × 39 and each digit is contained in the equation exactly once

**7256** is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors

**7260** is a doubly triangular numbers

**7269** is a value of n for which n and 2n together use each digit 1-9 exactly once

**7271** and its reverse are both differences of positive cubes

**7272** is a Kaprekar number (A006886)

**7281** is a value of n for which 3n and 7n together use each digit exactly once

**7285** has a 7^{th} power that contains the same digits as 544^{10}

**7286** is the number of subsets of {1,2,3,...,16} that have a sum divisible by 9

**7293** is a value of n for which n and 2n together use each digit 1-9 exactly once

**7295** is a value of n for which 4n and 5n together use each digit exactly once

**7297** is a Proth prime

**7306** is the smallest number whose 7^{th} power starts with 7 identical digits

**7311** is the number of symmetric plane partitions of 33

**7312** is a value of n for which n and 8n together use each digit 1-9 exactly once

**7314** is the smallest number so that it and its successor are both products of 4 distinct primes

**7315** = _{22}C _{4}

**7318** is the number of functions from 10 unlabeled points to themselves

**7320** is the number of triangles of any size contained in the triangle of side 30 on a triangular grid

**7321** is the number of intersections when all the diagonals of a regular 24-gon are drawn

**7322** is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole on a side

**7326** = 1 × 22 × 333

**7327** is a number whose sum of divisors is a 5^{th} power

**7329** is a value of n for which n and 2n together use each digit 1-9 exactly once

**7330** is the number of unsymmetrical ways to dissect a regular 14-gon into 12 triangles

**7331** is a right-truncatable prime

**7333** is a right-truncatable prime

**7336** is the number of ways to color the vertices of a triangle with 28 colors, up to rotation

**7337** is a hexagonal pyramidal number

**7338** is the closest integer to 17^{π }

**7339** has a 4^{th} power that is the sum of four 4^{th} powers

**7341** has the same digits as the 7341^{st} prime

**7342** is the number of ways to stack 29 pennies in contiguous rows so that each penny lies on the table or on two pennies

**7344** is a value of n for which 4n and 7n together use each digit exactly once

**7345** has the same digits as the 7345^{th} prime

**7351** is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

**7353** is the largest number n known so that both n and n^{3} have only odd digits.

**7356** is a value of n for which 5n and 7n together use each digit exactly once

**7358** is a composite number that remains composite when preceded or followed by any digit

**7359** is a Lucas 6-step number

**7360** can be written as the product of a number and its reverse in 2 different ways

**7361** is the number of ways to play the first 5 moves in Checkers

**7364** is a value of n for which n and 8n together use each digit 1-9 exactly once

**7366** is the maximum number of regions space can be divided into by 29 spheres

**7371** has a base 2 representation that begins with its base 9 representation

**7375** is a member of the Fibonacci -type sequence starting with 1 and 4

**7376** is a structured truncated tetrahedral number

**7380** is the number of numbers with 4 or fewer digits that do not contain any 0's

**7381** = 11111 in base 9

**7383** has a 4^{th} power that is 1/2 of the sum of three 4^{th} powers

**7384** has the same digits as the 7384^{th} prime

**7385** is a Keith number

**7387** is the product of two consecutive primes

**7393** is a right-truncatable prime

**7396** has a 4^{th} root whose decimal part starts with the digits 1-9 in some order

**7403** is the smallest number that can not be formed using the digit 1 at most 28 times, together with the symbols +, –, × and ÷

**7404** = 6 + 66 + 666 + 6666

**7410** = 361 + 362 + . . . + 380 = 381 + 382 + . . . + 399

**7413** is the number of even permutations on 8 elements with no fixed points

**7414** is a value of n for which φ (n) = φ (reverse(n))

**7416** is a value of n for which n and 8n together use each digit 1-9 exactly once

**7420** is the number of permutations of 8 items that fix 2 elements

**7421** is a value of n for which 4n and 5n together use each digit exactly once

**7422** is the sum of its proper divisors that contain the digit 7

**7424** and its successor are both abundant (A096399)

**7425** is an odd primitive abundant number (A091191, A006038)

**7427** is the number of inequivalent asymmetric Ferrers graphs with 35 points

**7429** is the product of 3 consecutive primes

**7430** is the number of labeled commutative monoids of order 5

**7433** is a prime that remains prime if any digit is deleted

**7435** is a cubic star number

**7436** is the number of 6×6 alternating sign matrices

**7444** is a value of n for which |cos(n)| is smaller than any previous integer

**7447** is a palindrome in base 2 and in base 10

**7448** is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

**7456** is the number of inequivalent Ferrers graphs with 35 points

**7462** is the number of multigraphs with 26 vertices and 4 edges

**7464** is a structured hexagonal diamond number

**7465** = 54321 in base 6

**7469** is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with integer dimensions less than 21

**7471** is a centered cube number

**7473** is a Tribonacci -like number starting from 1, 1, and 1

**7475** has a sum of digits equal to its largest prime factor

**7480** is a value of n for which _{2n}C _{n} is divisible by n^{2}

**7485** is the number of conjugacy classes of the alternating group A_{35}

**7488** = (12 × 13 × 14 × 15 × 16) / (12 + 13 + 14 + 15 + 16)

**7490** has a square with the last 3 digits the same as the 3 digits before that

**7491** has a base 8 representation which is the reverse of its base 7 representation

**7494** is the sum of its proper divisors that contain the digit 4

**7496** = 777 + 44 + 9 + 6666

**7497** is a hendecagonal pyramidal number

**7499** is the smallest number whose 8^{th} power has 31 digits

**7500** is the order of a perfect group

**7508** would be prime if preceded and followed by a 1, 3, 7, or 9

**7509** has a 6^{th} root whose decimal part starts with the digits 1-9 in some order

**7512** is the sum of its proper divisors that contain the digit 5

**7515** has the property that the sum of its prime factors is equal to the product of its digits

**7519** is a member of the Fibonacci -type sequence starting with 1 and 7

**7524** is the number of rectangles with corners on an 12×12 grid of points

**7525** has a square with the last 3 digits the same as the 3 digits before that

**7528** is the number of ways, up to rotation and reflection, of dissecting a regular 14-gon into 12 triangles

**7531** has digits in arithmetic sequence

**7532** has a square comprised of the digits 0-7

**7535** has a square whose digits each occur twice

**7541** is an Eisenstein-Mersenne prime (A066408)

**7542** is a value of n for which 4n and 7n together use each digit exactly once

**7546** is the number of series-reduced planted trees with 19 vertices

**7547** is the maximum number of regions a circle can be cut into by joining 21 points on the circumference with straight lines

**7549** is the largest known prime p where no numbers of the form p-n^{2} are prime

**7551** is a value of n for which φ (n) + φ (n+1) divides σ (n) + σ (n+1)

**7552** is the number of arrangements of 6 non-attacking queens on a 10×6 chessboard

**7557** is a palindrome that is the sum of the first 37 palindromes

**7560** is the smallest number with 64 divisors

**7561** is a Markov number

**7562** would be prime if preceded and followed by a 1, 3, 7, or 9

**7574** is the sum of consecutive squares in 2 ways

**7581** is the number of monotone Boolean functions of 5 variables

**7586** = 777 + 55 + 88 + 6666

**7588** is the smallest multiple of 28 whose digits add to 28

**7590** is a number whose sum of divisors is a 4^{th} power

**7595** is the number of simplicial polyhedra with 12 vertices

**7597** is a number whose sum of divisors is a 5^{th} power

**7600** is a substring of any power of itself

**7614** is a value of n for which n and 7n together use each digit 1-9 exactly once

**7615** is a value of n for which σ (n+1) = 2σ (n)

**7617** is a Hexanacci number

**7618** has a cube that contains only digits 4 and smaller.

**7620** is the number of multigraphs with 5 vertices and 14 edges

**7625** is a value of n for which σ (φ (n)) = 2σ (n)

**7627** is a value of n for which σ (φ (n)) = 2σ (n)

**7629** is a value of n for which n and 5n together use each digit 1-9 exactly once

**7632** is a value of n for which 5n and 6n together use each digit exactly once

**7635** is a centered tetrahedral number

**7639** is the number of rooted ternary trees with 13 vertices

**7647** is a Keith number

**7648** is the number of ways a 10×1 rectangle can be surrounded by 10×1 rectangles

**7650** can be written as the product of a number and its reverse in 2 different ways

**7651** is a value of n for which _{2n}C _{n} is not divisible by 3, 5, or 7

**7652** is a value of n for which n^{2} and n^{3} use the same digits

**7654** has digits in arithmetic sequence

**7658** is the largest number known that does not have any digits in common with its cube

**7659** is the number of planar graphs with 22 vertices, all with degree 5 or more

**7663** is the product of two primes which are reverses of each other

**7664** is the Entringer number E(8,6).

**7665** is a Kaprekar constant in base 2

**7667** is a palindrome in base 6 and in base 10

**7669** is the number of integers with complexity 31

**7672** = 777 + 6666 + 7 + 222

**7673** is the smallest number with the property that its first 8 multiples contain the digit 3

**7679** = 7 + 6666 + 7 + 999

**7680** is the number of possible rook moves on a 16×16 chessboard

**7681** is a Proth prime

**7683** is a truncated tetrahedral number

**7685** is the number of necklaces possible with 18 beads, each being one of 2 colors

**7686** is a value of n for which 7n and 9n together use each digit exactly once

**7688** is an Achilles number

**7692** is a value of n for which n and 2n together use each digit 1-9 exactly once

**7693** is a value of n for which the sum of the first n primes is a palindrome

**7695** and its successor are both divisible by 4^{th} powers

**7698** has a square with the first 3 digits the same as the next 3 digits

**7700** is a value of n for which 2φ (n) = φ (n+1)

**7703** has a 4^{th} power that is the sum of four 4^{th} powers

**7710** is the number of degree 17 irreducible polynomials over GF(2)

**7712** is the number of necklaces (that can't be turned over) possible with 17 beads, each being one of 2 colors

**7713** is a value of n for which 4n and 9n together use each digit exactly once

**7714** is the sum of the first 28 squares

**7721** is the smallest value of n for which 3^{n} contains 8 consecutive 3's

**7724** is the smallest number that can not be written using +, ×, and 5 Fibonacci numbers

**7727** is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged

**7732** and the two numbers before it and after it are all products of exactly 3 primes

**7734** is the sum of its proper divisors that contain the digit 8

**7736** is the number of labeled Eulerian digraphs with 5 vertices

**7738** has the property that dropping its first and last digits gives its largest prime factor

**7739** is a Padovan number

**7741** is the number of trees with 15 vertices

**7743** is the smallest number whose 9^{th} power has 35 digits

**7744** is the smallest known square with no isolated digits

**7745** and its reverse are both one more than a square

**7746** is the number permutations of {1,2,3,...,21} where adjacent numbers differ by no more than 2

**7752** is the generalized Catalan number C(14,5)

**7754** is the number of binary cube-free words of length 21

**7755** is the index of a prime Woodall number

**7765** is the number of ways to tile a 7×5 rectangle with integer -sided squares

**7770** = _{37}C _{3}

**7772** has a square root whose decimal part starts with the digits 1-9 in some order

**7775** = 55555 in base 6

**7776** is a 5^{th} power whose digits are non-increasing

**7777** is a Kaprekar number (A006886)

**7778** is the closest integer to 27^{e }

**7785** is a value of n for which 5n and 6n together use each digit exactly once

**7788** is the index of a triangular number containing only 3 different digits

**7792** has a square that is the sum of a cube and 5^{th} power

**7793** is the smallest prime so that it and the next 5 primes are all equal to 5 (mod 6)

**7795** has the same digits as the 7795^{th} prime

**7799** is a value of n for which |cos(n)| is smaller than any previous integer

**7800** is the order of a non-cyclic simple group

**7803** is an Achilles number

**7805** is the maximum number of pieces a torus can be cut into with 35 cuts

**7807** is the maximum number of regions a cube can be cut into with 36 cuts

**7808** is the number of 4×4 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner

**7810** has the property that its square is the concatenation of two consecutive numbers

**7811** is the number of ordered sequences of coins totaling 32 cents

**7812** = 222222 in base 5

**7820** is the Stirling number of the second kind S(17,15)

**7821** is a value of n for which 2n and 9n together use each digit exactly once

**7824** is a value of n for which 5n and 7n together use each digit exactly once

**7825** is a rhombic dodecahedral number

**7826** is the number of necklaces possible with 6 beads, each being one of 6 colors

**7827** has a square whose digits each occur twice

**7835** would be prime if preceded and followed by a 1, 3, 7, or 9

**7846** is a factor of 7847784878497850

**7848** is the number of connected 5-regular graphs with 12 vertices

**7849** is the number of connected 6-regular graphs with 12 vertices

**7851** = 7777 + 8 + 55 + 11

**7852** = 1963 × 4, and each digit from 1-9 is contained in the equation exactly once

**7853** is the largest prime factor of 11! - 1

**7854** is a number whose sum of divisors is a 4^{th} power

**7856** and its successor are both the product of a prime and the 4^{th} power of a prime

**7860** is the number of nonisomorphic 3-state automata with binary inputs and outputs

**7874** is the smallest number n for which n concatenated with n+2 is a square

**7875** is an odd abundant number (A005101, A005231)

**7880** is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 26 stamps

**7882** is a structured pentagonal hexacontahedral number

**7884** is a value of n for which 2n and 5n together use each digit exactly once

**7887** is the index of a pentagonal number which is twice another pentagonal number

**7888** is a value of n where φ (n) is the product of the digits of n

**7890** is an icosahedral number

**7894** is a value of n for which n and 8n together use each digit 1-9 exactly once

**7895** is the number of multigraphs with 6 vertices and 11 edges

**7905** is a Kaprekar constant in base 2

**7908** has the same digits as the 7908^{th} prime

**7909** is a Keith number

**7912** is a weird number

**7913** is a value of n for which σ (n-1) = σ (n+1)

**7917** is the number of partitions of 57 into distinct parts

**7919** is the 1000^{th} prime

**7920** is the order of the smallest sporadic group

**7921** is the square of a Fibonacci number

**7922** has the property that the sum of its prime factors is equal to the product of its digits

**7923** is a value of n for which n and 2n together use each digit 1-9 exactly once

**7926** is the diameter of the earth in miles

**7928** is a Friedman number

**7931** is a heptagonal pyramidal number

**7932** is a value of n for which n and 2n together use each digit 1-9 exactly once

**7936** is the 5^{th} tangent number

**7937** is the smallest number whose cube contains 5 consecutive 9's

**7939** , when followed by any of its digits, is prime

**7941** = 7777 + 9 + 44 + 111

**7942** = 7777 + 99 + 44 + 22

**7946** = 7777 + 99 + 4 + 66

**7953** is the number of domino tilings of a 3×14 rectangle

**7954** is the smallest value of n for which 5^{n} + n is prime

**7956** is a value of n for which n and 4n together use each digit 1-9 exactly once

**7957** is a Poulet number

**7960** is a structured deltoidal hexacontahedral number

**7964** is a value of n for which φ (n) = φ (reverse(n))

**7969** has a square that is formed by 3 squares that overlap by 1 digit

**7980** is the smallest number whose divisors contain every digit at least 7 times

**7983** is a Lucas 8-step number

**7986** = 11 × 22 × 33

**7992** can be written as the difference between two positive cubes in more than one way

**7993** is one less than twice its reverse

**7994** has a 5^{th} power that is closer to a cube than a square

**7997** is a palindrome in base 4 and in base 10

**7999** , when followed by any of its digits, is prime