This site is supported by donations to The OEIS Foundation.

# Annotated version of "What's Special About This Number?" (Part 9)

## 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 9: The Numbers 9000 to 9999

**9000** is the index of a triangular number containing only 3 different digits

**9002** is a value of n such that n(n+7) is a palindrome

**9005** is the number of inequivalent Ferrers graphs with 36 points

**9006** is a strobogrammatic number

**9009** is a centered cube number

**9011** has a square that is the concatenation of two consecutive odd numbers

**9012** is the sum of its proper divisors that contain the digit 5

**9016** is the number of perfect squared rectangles of order 16

**9018** has a square with the last 3 digits the same as the 3 digits before that

**9020** is the number of ways to color the vertices of a triangle with 30 colors, up to rotation

**9023** has the property that the concatenation of its prime factors in increasing order is a square

**9024** is the number of regions formed when all diagonals are drawn in a regular 24-gon

**9025** is a Friedman number

**9028** is the number of ways to tile a 9×4 rectangle with integer -sided squares

**9032** would be prime if preceded and followed by a 1, 3, 7, or 9

**9036** has a 9^{th} power that contains the same digits as 3585^{10}

**9037** is a value of n for which 2n and 7n together use each digit exactly once

**9038** is the number of conjugacy classes of the alternating group A_{36}

**9042** is the trinomial coefficient T(11,4)

**9045** is the number of ways to 18-color the faces of a tetrahedron

**9048** is the number of regions the complex plane is cut into by drawing lines between all pairs of 24^{th} roots of unity

**9049** is an Eisenstein-Mersenne prime (A066408, A066408)

**9052** is the maximum number of regions space can be divided into by 31 spheres

**9055** is the index of a triangular number containing only 3 different digits

**9056** is a cubic star number

**9059** has an 8^{th} root that starts 3.12345...

**9070** has a 4^{th} root whose decimal part starts with the digits 1-9 in some order

**9072** has a base 2 and base 3 representation that end with its base 6 representation

**9073** has a base 2 and base 3 representation that end with its base 6 representation

**9074** has a base 3 representation that ends with its base 6 representation

**9077** is a Markov number

**9078** has a cube whose digits occur with the same frequency

**9079** has a square that is the concatenation of two consecutive decreasing numbers

**9086** is the number of regions formed when all diagonals are drawn in a regular 23-gon

**9091** is the unique prime whose reciprocal has period 10

**9093** has a square with the first 3 digits the same as the next 3 digits

**9099** is the number of ways to 3-color the faces of a dodecahedron

**9101** has a square where the first 6 digits alternate

**9104** has a square with the first 3 digits the same as the next 3 digits

**9105** is the number of possible positions in Checkers after 6 moves

**9108** is a heptagonal pyramidal number

**9109** is the number of regions the complex plane is cut into by drawing lines between all pairs of 23^{rd} roots of unity

**9113** is a narcissistic number in base 5

**9115** has a base 3 representation that begins with its base 6 representation

**9116** is a strobogrammatic number

**9117** is a value of n for which 6n and 7n together use each digit exactly once

**9119** is the number of symmetric plane partitions of 34

**9121** is the number of possibilities for the last 5 digits of a square

**9126** is a pentagonal pyramidal number

**9134** has a 10^{th} root whose decimal part starts with the digits 1-9 in some order

**9135** is a value of n for which 2n and 7n together use each digit exactly once

**9137** has a 4^{th} power that is the sum of four 4^{th} powers

**9139** = _{39}C _{3}

**9152** = A068782(18) and its successor are both divisible by 4^{th} powers

**9153** is a value of n for which 2n and 3n together use each digit exactly once

**9154** is a value of n for which φ (n) and σ (n) are square

**9156** is a value of n for which n and 8n together use each digit 1-9 exactly once

**9158** is a value of n for which n and 8n together use each digit 1-9 exactly once

**9162** is a value of n for which 5n and 8n together use each digit exactly once

**9168** = 27504 / 3, and each digit is contained in the equation exactly once

**9172** is the number of connected planar maps with 7 edges

**9174** is the sum of its proper divisors that contain the digit 5

**9176** is the maximum number of pieces a torus can be cut into with 37 cuts

**9178** is the maximum number of regions a cube can be cut into with 38 cuts

**9179** is a value of n for which φ (n) = φ (n-1) + φ (n-2)

**9182** is a value of n for which 4n and 5n together use each digit exactly once

**9183** is the number of sets of distinct positive integers with mean 8

**9185** is a value of n for which 2n and 7n together use each digit exactly once

**9189** is the number of sided 10-ominoes

**9191** is not the sum of a square , a cube , a 4^{th} power, and a 5^{th} power

**9196** has the property that dropping its first and last digits gives its largest prime factor

**9198** is the number of ternary square-free words of length 25

**9201** is a truncated octahedral number

**9214** = A001524(30) is the number of ways to stack 30 pennies in contiguous rows so that each penny lies on the table or on two pennies

**9216** is a Friedman number

**9217** is the total number of digits of all binary numbers of length 1-10

**9219** is a value of n for which |cos(n)| is smaller than any previous integer

**9224** is an octahedral number

**9233** is the number of different arrangements (up to rotation and reflection) of 13 non-attacking queens on a 13×13 chessboard

**9234** is the number of multigraphs with 7 vertices and 10 edges

**9235** is the number of 13-iamonds

**9237** is a value of n for which n and 5n together use each digit 1-9 exactly once

**9240** = _{22}P _{3}

**9241** is a Cuban prime

**9243** has a 4^{th} power that is the sum of four 4^{th} powers

**9248** is the number of possible rook moves on a 17×17 chessboard

**9250** = (10^{3} + 10^{4} + 10^{5} + 10^{6}) / (3 × 4 × 5 × 6)

**9251** has a square whose digits each occur twice

**9252** is the number of necklaces with 10 white and 10 black beads

**9253** is the smallest number that appears in its factorial 9 times

**9261** is a Friedman number

**9267** is a value of n for which n and 2n together use each digit 1-9 exactly once

**9268** is a value of n for which 2φ (n) = φ (n+1)

**9272** is a weird number

**9273** is a value of n for which n and 2n together use each digit 1-9 exactly once

**9282** is the product of three consecutive Fibonacci numbers

**9284** is the number of ways to place 2 non-attacking bishops on a 12×12 chessboard

**9285** is the number of 16-hexes with reflectional symmetry

**9286** is a narcissistic number in base 7

**9287** is the number of stretched 10-ominoes

**9288** can be written as the sum of 2, 3, 4, or 5 positive cubes

**9289** is a Tetranacci -like number starting from 1, 1, 1, and 1

**9298** has the property that the concatenation of its prime factors in increasing order is a square

**9304** = 65128 / 7, and each digit is contained in the equation exactly once

**9305** has the property that if each digit is replaced by its square , the resulting number is a square

**9306** is a value of n for which 3n and 5n together use each digit exactly once

**9310** is a decagonal pyramidal number

**9311** is the index of a prime Fibonacci number

**9313** , when followed by any of its digits, is prime

**9314** is the 13^{th} Iccanobif number

**9315** is a value of n for which 2n and 3n together use each digit exactly once

**9316** is a value of n for which n and 8n together use each digit 1-9 exactly once

**9321** is a value of n for which n and 8n together use each digit 1-9 exactly once

**9324** is the reciprocal of the sum of the reciprocals of 14652 and its reverse

**9327** is a value of n for which n and 2n together use each digit 1-9 exactly once

**9330** is the Stirling number of the second kind S(10,3)

**9331** has the property that the sum of its prime factors is equal to the product of its digits

**9339** is a value of n for which φ (n) = φ (n-2) - φ (n-1)

**9347** is a value of n for which the sum of square -free divisors of n and n+1 are the same

**9348** has a 8^{th} power that contains the same digits as 3588^{9}

**9349** is the 19^{th} Lucas number

**9350** appears inside its 4^{th} power

**9352** is a value of n for which n and 8n together use each digit 1-9 exactly once

**9360** is a value of n for which σ (n-1) = σ (n+1)

**9362** = 22222 in base 8

**9363** is the number of tilted rectangles with vertices in a 15×15 grid

**9364** is the number of connected digraphs with 5 vertices

**9367** is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors

**9371** is a prime that remains prime when preceded and followed by one, two, three, or four 3's

**9374** is a value of n for which φ (σ (n)) = φ (n)

**9375** has a cube that ends with those digits

**9376** is an automorphic number

**9377** is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

**9378** is a value of n for which 4n and 5n together use each digit exactly once

**9380** is the number of lines through exactly 2 points of a 15×15 grid of points

**9382** is a value of n for which 4n and 5n together use each digit exactly once

**9383** is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged

**9385** is the sum of consecutive squares in 2 ways

**9386** = 99 + 333 + 8888 + 66

**9387** is a Smith brother

**9391** has a square with the first 3 digits the same as the last 3 digits

**9393** is the number of non-isomorphic 3×3×3 Rubik's cube positions that require exactly 5 quarter turns to solve

**9394** is a value of n so that n(n+8) is a palindrome

**9396** is the number of symmetric 3×3 matrices in base 6 with determinant 0

**9403** = 65821 / 7, and each digit is contained in the equation exactly once

**9406** is the index of a triangular number containing only 3 different digits

**9407** has a 7^{th} root whose decimal part starts with the digits 1-9 in some order

**9408** is the number of reduced 6×6 Latin squares (A000315)

**9413** has a cube whose digits occur with the same frequency

**9415** is the sum of the first 19 numbers that have digit sum 19

**9416** is a value of n for which n and 8n together use each digit 1-9 exactly once

**9421** is a value of n for which n and 8n together use each digit 1-9 exactly once

**9424** has the property that the fractional part of π ^{9424} begins .9424...

**9426** is a value of n for which 5n and 7n together use each digit exactly once

**9427** is the smallest number that can not be formed using the digit 1 at most 29 times, together with the symbols +, –, × and ÷

**9428** is the smallest number whose square begins with four 8's

**9431** is a number n for which n, n+2, n+6, and n+8 are all prime

**9432** is the number of 3-colored rooted trees with 6 vertices

**9436** is the smallest number whose 15^{th} power contains exactly the same digits as another 15^{th} power

**9439** is prime , and 5 closest primes are all smaller

**9444** has a square with the first 3 digits the same as the next 3 digits

**9445** is the closest integer to 29^{e }

**9450** is the denominator of ζ (8) / π ^{8}

**9451** is the number of binary rooted trees with 19 vertices

**9452** is the smallest number whose cube contains 5 consecutive 4's

**9455** is the sum of the first 30 squares

**9465** is an hexagonal prism number

**9468** is the sum of its proper divisors that contain the digit 7

**9471** is an octagonal pyramidal number (A002414)

**9473** is a Proth prime

**9474** is a narcissistic number

**9477** is the maximum determinant of a binary 13×13 matrix

**9481** is a number whose sum of divisors is a 4^{th} power

**9489** is the closest integer to π ^{8}

**9493** is a member of the Fibonacci -type sequence starting with 1 and 9

**9496** is the number of 10×10 symmetric permutation matrices

**9497** is the number of bicentered trees with 16 vertices

**9499** has a 5^{th} power whose first few digits are 77337377...

**9500** is a hexagonal pyramidal number

**9504** is a betrothed number

**9513** is the smallest number without increasing digits that is divisible by the number formed by writing its digits in increasing order

**9519** has a 4^{th} power that is the sum of four 4^{th} powers

**9520** is an enneagonal pyramidal number

**9523** is a value of n for which 4n and 5n together use each digit exactly once

**9529** is the number of 3×3 sliding puzzle positions that require exactly 18 moves to solve starting with the hole in a corner

**9531** is the index of a prime Woodall number

**9538** is a value of n for which 4n and 5n together use each digit exactly once

**9541** is a value of n for which n and 8n together use each digit 1-9 exactly once

**9542** is the number of ways to place a non-attacking white and black pawn on a 11×11 chessboard

**9551** has the same digits as the 9551^{st} prime

**9552** and the following 34 numbers are composite

**9555** is an odd primitive abundant number (A091191, A006038)

**9563** = 9 + 5555 + 666 + 3333

**9564** is the number of paraffins with 10 carbon atoms

**9568** = 9 + 5 + 666 + 8888

**9574** is a value of n for which |cos(n)| is smaller than any previous integer

**9576** = 19!!!!!

**9583** is the number of subsets of {1, 2, 3, ... 20} that do not contain solutions to x + y = z

**9592** is the number of primes with 5 or fewer digits

**9596** is the index of a triangular number containing only 3 different digits

**9601** is a Proth prime

**9602** has the property that if each digit is replaced by its square, the resulting number is a square

**9605** , when concatenated with 4 less than itself, is square

**9608** is the number of digraphs with 5 vertices

**9615** is the smallest number whose cube starts with 5 identical digits

**9616** is an icosahedral number

**9623** is the number of symmetric 10-cubes

**9625** has a square formed by inserting a block of digits inside itself

**9627** is a value of n for which n and 5n together use each digit 1-9 exactly once

**9629** is a value of n for which 2n and 7n together use each digit exactly once

**9632** is the number of different arrangements of 4 non-attacking queens on a 4×14 chessboard

**9633** is a Smith brother

**9634** is a Smith brother

**9639** has a 4^{th} power that is the sum of four 4^{th} powers

**9643** is the smallest number that can not be formed using the numbers 2^{0}, 2^{1}, ... , 2^{7}, together with the symbols +, –, × and ÷

**9648** is a factor of the sum of the digits of 9648^{9648}

**9653** = 99 + 666 + 5555 + 3333

**9658** = 99 + 666 + 5 + 8888

**9660** is a truncated tetrahedral number

**9670** is the number of 8-digit triangular numbers

**9673** is the number of triangles of any size contained in the triangle of side 33 on a triangular grid

**9677** is a prime that remains prime if any digit is deleted

**9682** is a value of n for which n!! - 1 is prime

**9689** is the exponent of a Mersenne prime (A000043, A000668)

**9691** has the property that the concatenation of its prime factors in increasing order is a square

**9695** is the sum of the digits of 5^{55}

**9696** is a strobogrammatic number

**9700** is the number of inequivalent 4-digit strings, where two strings are equivalent if turning one upside down gives the other

**9701** has a square whose digits each occur twice

**9707** does not occur in its factorial in base 2

**9709** has a cube whose digits occur with the same frequency

**9711** uses the same digits as π (9711)

**9716** is the number of Pyramorphix puzzle positions that require exactly 5 moves to solve

**9720** is the order of a perfect group

**9721** is the largest prime factor of 1234567

**9723** is a value of n for which n and 5n together use each digit 1-9 exactly once

**9724** = 1111 in base 21

**9726** is the smallest number in base 5 whose square contains the same digits in the same proportion

**9728** can be written as the sum of 2, 3, 4, or 5 positive cubes

**9738** is the number of trees on 22 vertices with diameter 5 (A000147)

**9747** is an Achilles number (A052486)

**9748** is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 14 stamps (A001211)

**9751** is the number of possible configurations of pegs (up to symmetry) after 8 jumps in solitaire (A112737)

**9753** is a value of n for which 4n and 5n together use each digit exactly once

**9754** is the number of paths between opposite corners of a 3×5 rectangle graph (A013992)

**9760** can be written as the product of a number and its reverse in 2 different ways (A066531)

**9764** would be prime if preceded and followed by a 1, 3, 7, or 9 (A059677)

**9765** is an odd primitive abundant number (A091191, A006038)

**9767** is the largest 4 digit prime composed of concatenating two 2 digit primes (A168499)

**9768** = 2 × 22 × 222 (A084034)

**9770** is the number of Hamiltonian cycles of a 4×12 rectangle graph (A006864)

**9775** is a number n so that the sum of the digits of n^{n}-1 is divisible by n (A109675)

**9777** is the number of graphs on 8 vertices with no isolated vertices (A006651)

**9779** has a square root that has four 8's immediately after the decimal point

**9784** is the number of 2 state Turing machines which halt (A004147)

**9786** has a square whose digits each occur twice (A052049)

**9789** is the smallest number that appears in its factorial 11 times (A061014)

**9790** is the number of ways to place 2 non-attacking kings on a 12×12 chessboard (A061995)

**9792** is the number of partitions of 59 into distinct parts (A078408)

**9793** is the smallest number that can be written as the sum of 4 distinct positive cubes in 5 ways (A025421)

**9796** has the property that dropping its first and last digits gives its largest prime factor (A114565)

**9797** is the product of two consecutive primes (A006094)

**9798** is a number whose sum of divisors is a 4^{th} power (A019422)

**9799** is a number whose sum of squares of the divisors is a square (A046655)

**9800** is the largest 4-digit number with single digit prime factors (A085868)

**9801** is 9 times its reverse (A031877)

**9802** , when concatenated with one less than it, is square (A054214)

**9805** is the number of subsequences of {1,2,3,...15} in which every odd number has an even neighbor (A007483)

**9809** is a stella octangula number (A007588)

**9823** is the number of centered trees with 16 vertices (A000676)

**9828** is the order of a non-cyclic simple group (A001034)

**9831** has a base 6 representation which is the reverse of its base 5 representation

**9839** would be prime if preceded and followed by a 1, 3, 7, or 9 (A059677, A059694)

**9841** = 111111111 in base 3 (A125118, A055129, A003462)

**9843** is the number of vertices in a Sierpinski triangle of order 8 (A067771)

**9849** is a centered tetrahedral number (A005894)

**9854** is the index of a triangular number containing only 3 different digits (A119207)

**9855** is a rhombic dodecahedral number (A005917)

**9856** is the number of ways to place 2 non-attacking knights on a 12×12 chessboard (A172132)

**9857** is a Proth prime (A080076)

**9858** is a number whose sum of divisors is a 4^{th} power (A019422)

**9861** is a dodecagonal pyramidal number (A007587)

**9862** is the number of knight's tours on a 6×6 chessboard (A001230)

**9865** is the number of digits in the 15^{th} Fermat number (A057755)

**9868** is the number of hydrocarbons with 10 carbon atoms (A002986)

**9871** is the largest 4-digit prime with different digits (A007810)

**9872** = 8 + 88 + 888 + 8888 (A099675)

**9876** is the largest 4-digit number with different digits

**9877** has a 4^{th} power that is the sum of four 4^{th} powers (A039664)

**9878** has a 10^{th} power whose first few digits are 88448448...

**9880** = _{40}C _{3} (A010990, A004337)

**9886** is a strobogrammatic number (A000787)

**9888** is the number of connected graphs with 8 vertices whose complements are also connected (A054915)

**9894** is the number of 3-colored trees with 7 vertices (A038060)

**9896** is the number of Pyraminx puzzle positions that require exactly 6 moves to solve (A079744)

**9900** = 10011010101100_{2} = 9900_{10} = 1881_{19} = 1199_{21}, each using two digits the same number of times

**9901** is the only prime known whose reciprocal has period 12 (A046107, A007615)

**9910** is the number of fixed 9-ominoes (A001168)

**9911** has the property that the sum of its prime factors is equal to the product of its digits (A067173, A065774)

**9912** is the number of graceful permutations of length 14 (A006967)

**9913** , when followed by any of its digits, is prime (A007811)

**9918** is the maximum number of pieces a torus can be cut into with 38 cuts (A003600)

**9919** can be written as the difference between two positive cubes in more than one way (A034179, A038864)

**9920** is the maximum number of regions a cube can be cut into with 39 cuts (A000125)

**9928** is a value of n for which reverse(φ (n)) = φ (reverse(n)) (A069282)

**9929** is the number of 3×3 sliding puzzle positions that require exactly 26 moves to solve starting with the hole on a side (A089483)

**9933** = 441 + 442 + . . . + 462 = 463 + 464 + . . . + 483 (A059270)

**9941** is the exponent of a Mersenne prime (A000043, A000668)

**9944** = 10011011011000_{2} = 9944_{10} = 2E2E_{15} = 11BB_{21}, each using two digits the same number of times

**9951** is the number of ways to color the vertices of a triangle with 31 colors, up to rotation (A006527)

**9959** is a member of the Fibonacci -type sequence starting with 2 and 5 (A001060)

**9960** is the number of 3×3×3 sliding puzzle positions that require exactly 8 moves to solve (A090573)

**9966** is the largest 4-digit strobogrammatic number (A000787)

**9973** is the largest 4-digit prime (A003618)

**9976** has a square formed by inserting a block of digits inside itself (A045953, A046838)

**9984** is the maximum number of regions space can be divided into by 32 spheres (A046127)

**9985** is the number of hyperbolic knots with 13 crossings (A052408)

**9988** is the number of prime knots with 13 crossings (A002863)

**9992** is the number of 2×2×2 Rubik's cube positions that require exactly 5 moves to solve (A079761)

**9995** has a square formed by inserting a block of digits inside itself (A045953, A046838)

**9996** has a square formed by inserting a block of digits inside itself (A045953, A046838)

**9998** is the smallest number n for which the concatenation of n, (n+1), ... (n+21) is prime (A052079)

**9999** is a Kaprekar number (A006886) (A006886)