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# Annotated version of "What's Special About This Number?" (Part 4)

## 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 4: The Numbers 4000 to 4999

**4000** has a cube that contains only even digits

**4002** has a square with the first 3 digits the same as the next 3 digits

**4004** = (10 × 11 × 12 × 13 × 14) / (10 + 11 + 12 + 13 + 14)

**4005** is a triangular number whose internal digits are triangular and whose external digits are triangular

**4006** = _{14}C _{4} + _{14}C _{0} + _{14}C _{0} + _{14}C _{6}

**4008** has a square with the last 3 digits the same as the 3 digits before that

**4010** is the magic constant of a 20×20 magic square

**4011** is the sum of the squares of 3 consecutive primes

**4013** is a prime factor of 1111111111111111111111111111111111

**4019** is a prime that remains prime if any digit is deleted

**4023** is the number of ways to tile a 3×23 rectangle with 3×1 rectangles

**4029** is the number of regions formed when all diagonals are drawn in a regular 19-gon

**4030** is a weird number

**4031** is the sum of the cubes of the first 6 primes

**4032** is the number of connected bipartite graphs with 10 vertices

**4033** is a Poulet number

**4037** is a member of the Fibonacci -type sequence starting with 1 and 6

**4040** is an enneagonal pyramidal number

**4047** is a hexagonal pyramidal number

**4048** is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

**4050** has the property that dropping its first and last digits gives its largest prime factor

**4051** is the number of partitions of 6 items into ordered lists

**4052** is the closest integer to sinh(9).

**4053** has a cube that contains only digits 5 and larger.

**4055** is the smallest number whose cube contains six 6's

**4056** is the number of possible rook moves on a 13×13 chessboard

**4059** is the sum of 3 consecutive cubes

**4060** = _{30}C _{3}

**4062** is the smallest number with the property that its first 8 multiples contain the digit 2

**4063** is a Tribonacci -like number starting from 1, 1, and 1

**4064** is a value of n for which σ (n) = σ (reverse(n))

**4068** is the number of ways to write 26 as the ordered sum of positive squares

**4071** is the number of ways to color the vertices of a triangle with 23 colors, up to rotation

**4074** is a value of n for which σ (n) = 2reverse(n)

**4077** has a square whose digits each occur twice

**4080** = _{17}P _{3}

**4083** is the number of ways 12 people can line up so that only one person has a taller person in front of him

**4086** is a permutation of the sum of its proper divisors

**4087** is the product of two consecutive primes

**4088** is the maximum number of pieces a torus can be cut into with 28 cuts

**4089** is a centered octahedral number

**4090** is the maximum number of regions a cube can be cut into with 29 cuts

**4093** = 28651 / 7, and each digit is contained in the equation exactly once

**4094** is the Entringer number E(8,2).

**4095** and its reverse are both differences of positive 4^{th} powers. It is also
the largest number of the form 2^{k}−1 (A000225) which is also a triangular number (A000217). (I.e. the last member of A076046)

**4096** is the smallest number with 13 divisors

**4097** is the smallest number (besides 2) that can be written as the sum of two cubes or the sum of two 4^{th} powers

**4098** is the number of subsets of the 26^{th} roots of unity that add to 1

**4099** has a square with the last 3 digits the same as the 3 digits before that

**4100** = 5555 in base 9

**4104** can be written as the sum of 2 cubes in 2 ways

**4106** is a Friedman number

**4112** is the number of necklaces possible with 17 beads, each being one of 2 colors

**4116** is the number of necklaces (that can't be turned over) possible with 16 beads, each being one of 2 colors

**4119** times the 4119^{th} prime is a palindrome .

**4120** has a cube with a digit sum larger than its 7^{th} power

**4121** is a number whose product of digits is equal to its sum of digits

**4122** is the number of labeled monoids of order 5 with fixed identity

**4124** is the number of binary partitions of 40

**4128** is the smallest number with the property that its first 10 multiples contain the digit 2

**4132** is the number of connected 3-regular bipartite graphs with 22 vertices

**4140** is the 8^{th} Bell number

**4141** = 4141_{5} + 4141_{7} + 4141_{8}

**4147** is a value of n for which φ (n) = φ (reverse(n))

**4149** is a value of n for which σ (n-1) = σ (n+1)

**4150** = 4^{5} + 1^{5} + 5^{5} + 0^{5}

**4151** = 4^{5} + 1^{5} + 5^{5} + 1^{5}

**4152** = 4^{5} + 1^{5} + 5^{5} + 2

**4153** = 4^{5} + 1^{5} + 5^{5} + 3

**4154** = 4^{5} + 1^{5} + 5^{5} + 4

**4155** = 4^{5} + 1^{5} + 5^{5} + 5

**4156** = 4^{5} + 1^{5} + 5^{5} + 6

**4157** = 4^{5} + 1^{5} + 5^{5} + 7

**4158** = 4^{5} + 1^{5} + 5^{5} + 8

**4159** = 4^{5} + 1^{5} + 5^{5} + 9

**4160** = 4^{3} + 16^{3} + 0^{3}

**4161** = 4^{3} + 16^{3} + 1^{3}

**4163** is the number of inequivalent asymmetric Ferrers graphs with 32 points

**4167** is a Friedman number

**4175** has a square comprised of the digits 0-7

**4176** has an 8^{th} root whose decimal part starts with the digits 1-9 in some order

**4180** is the sum of the first 17 Fibonacci numbers

**4181** is the first composite number in the Fibonacci sequence with a prime index

**4183** is a narcissistic number in base 7

**4185** is the smaller number in a Ruth-Aaron pair

**4186** is a hexagonal , 13-gonal, triangular number

**4187** is the smallest Rabin-Miller pseudoprime with an odd reciprocal period

**4188** is a value of n for which σ (n-1) = σ (n+1)

**4191** is the number of graphs with 12 vertices and 10 edges

**4192** is the larger number in a Ruth-Aaron pair

**4193** is the number of 3×3 sliding puzzle positions that require exactly 16 moves to solve starting with the hole on a side

**4195** has a sum of prime factors that is equal to the sum of the prime factors of the two preceding numbers

**4196** is the number of 3-regular bipartite graphs with 22 vertices

**4199** is the product of 3 consecutive primes

**4200** is divisible by its reverse

**4202** = 4202_{5} + 4202_{7} + 4202_{8}

**4204** and the two numbers before it and after it are all products of exactly 3 primes

**4205** has the property that if each digit is replaced by its square , the resulting number is a square

**4207** is the number of cubic graphs with 16 vertices

**4209** is the number of conjugacy classes of the alternating group A_{32}

**4210** is the number of graphs with 10 vertices with clique number 7

**4211** is a number whose product of digits is equal to its sum of digits

**4215** is a centered dodecahedral number

**4216** is an octagonal pyramidal number (A002414)

**4217** is the smallest number whose 8^{th} power has 29 digits

**4219** is a Cuban prime

**4220** is a number n for which the sum of the first n composite numbers is a palindrome

**4222** is the number of 13-hexes with bilateral symmetry

**4223** is the maximum number of 12^{th} powers needed to sum to any number

**4224** is a palindrome that is one less than a square

**4225** is the smallest number that can be written as the sum of two squares in 12 ways

**4231** is the number of labeled partially ordered sets with 5 elements

**4232** is the number of different products of subsets of the set {1, 2, 3, ... 16}

**4233** is a heptagonal pyramidal number

**4235** has a cube that contains only digits 5 and larger.

**4236** has a 4^{th} power that is the sum of four 4^{th} powers

**4237** is the number of ordered sequences of coins totaling 30 cents

**4240** is a Leyland number

**4243** = 444 + 22 + 444 + 3333

**4244** is the total number of digits in all the 4-digit primes

**4249** is a value of n for which |cos(n)| is smaller than any previous integer

**4252** is the smallest number in base 8 to have 5 different digits

**4253** is the exponent of a Mersenne prime (A000043, A000668)

**4254** is the number of 7-drafters

**4255** is a centered tetrahedral number

**4257** is the number of triangles formed by connecting the diagonals of a regular 11-gon

**4258** is the sum of the digits of the 18^{th} Mersenne prime (A066538)

**4260** is a value of n for which n+1, 2n+1, 3n+1, and 4n+1 are all prime

**4264** is a number whose sum of squares of the divisors is a square

**4267** has a 4^{th} power that is the sum of four 4^{th} powers

**4269** has a cube whose first few digits are 77799797...

**4278** does not occur in its factorial in base 2

**4279** is the smallest semiprime super Catalan number

**4280** has a square root whose decimal part starts with the digits 0-9 in some order

**4283** is the smallest number with complexity 29

**4285** is a structured hexagonal diamond number

**4290** is a value of n for which _{2n}C _{n} is divisible by n^{2}

**4291** is the number of necklaces possible with 6 beads, each being one of 6 colors

**4293** has exactly the same digits in 3 different bases

**4294** is a value of n for which σ (n) = φ (n) + φ (n-1) + φ (n-2)

**4297** is the smallest prime that is followed by 29 composite numbers .

**4300** has the property that if each digit is replaced by its square , the resulting number is a square

**4303** is the number of triangles of any size contained in the triangle of side 25 on a triangular grid

**4305** has exactly the same digits in 3 different bases

**4310** has exactly the same digits in 3 different bases

**4311** is the largest number n known with the property that n-2^{k} is a pseudoprime for all k>0

**4312** is the smallest number whose 10^{th} power starts with 7 identical digits

**4320** = (6+4) × (6+3) × (6+2) × (6+0)

**4321** has digits in arithmetic sequence

**4324** is the sum of the first 23 squares

**4325** is a member of the Fibonacci -type sequence starting with 4 and 9

**4329** is the only number n so that n, 2n, 4n, and 6n together contain every digit 1-9 exactly twice

**4330** is the number of 4-regular multigraphs with 10 vertices

**4332** = 444 + 3333 + 333 + 222

**4333** has a 4^{th} power that is the sum of four 4^{th} powers

**4335** = 444 + 3333 + 3 + 555

**4336** = 4 + 3333 + 333 + 666

**4337** is a value of n for which φ (n) = φ (n-1) + φ (n-2)

**4339** = 4 + 3333 + 3 + 999

**4340** is the number of 3×3 sliding puzzle positions that require exactly 27 moves to solve starting with the hole in the center

**4342** appears inside its 4^{th} power

**4343** has the property that the sum of its prime factors is equal to the product of its digits

**4347** is a value of n for which 2n and 5n together use the digits 1-9 exactly once

**4348** is the number of ways of placing 24 points on a 12×12 grid so that no 3 points are on a line

**4352** has a cube that contains only even digits

**4355** = 2^{4} + 3^{5} + 4^{6}

**4356** is two thirds of its reverse

**4357** is the smallest number with the property that its first 5 multiples contain the digit 7

**4359** is a perfect totient number

**4361** is the number of different degree sequences for graphs with 9 vertices

**4364** is a value of n for which σ (n) = σ (n+1)

**4365** is a value of n for which 4n and 9n together use each digit exactly once

**4368** = _{16}C _{5}

**4369** is an odd number for which a regular polygon is constructible by straightedge and compass

**4371** is a Poulet number

**4374** and its successor are both divisible by 4^{th} powers

**4375** is a perfect totient number

**4376** and its reverse are both differences of positive cubes

**4380** is the number of ways to place 2 non-attacking bishops on a 10×10 chessboard

**4381** is a stella octangula number

**4382** is the number of primitive sorting networks on 9 elements

**4388** divides 1^{1} + 2^{2} + 3^{3} + ^{ . . .} + 4388^{4388}

**4390** is a house number

**4392** is a value of n for which n and 4n together use each digit 1-9 exactly once

**4394** is a truncated square pyramid number

**4396** = 157 × 28 and each digit is contained in the equation exactly once

**4398** is the number of subsets of {1, 2, 3, ... 18} that do not contain solutions to x + y = z

**4402** has the property that if each digit is replaced by its square , the resulting number is a square

**4406** is the number of divisors of the 16^{th} perfect number

**4408** is the number of 20-iamonds with bilateral symmetry

**4410** is a Padovan number

**4413** is the index of a prime Euclid number

**4418** is the number of 7-nons

**4421** = 7! - 6! + 5! - 4 ! + 3! - 2! + 1!

**4422** is the maximum value of n so that there exist 5 denominations of stamps so that every postage from 1 to n can be paid for with at most 15 stamps

**4423** is the exponent of a Mersenne prime (A000043, A000668)

**4424** 2^{5} + 3^{5} + 4^{5} + 5^{5}

**4425** is the sum of the first five 5^{th} powers

**4430** is the rectilinear crossing number of complete graph K_{25}

**4431** is the number of graphs with 8 vertices that have 2 automorphisms

**4434** is the sum of its proper divisors that contain the digit 7

**4435** uses the same digits as φ (4435)

**4436** is the number of ways to place 4 non-attacking knights on a 5×5 chessboard

**4438** is the number of 15-hexes with reflectional symmetry

**4441** is the number of different solutions to ±1±2...±18 = 1

**4442** is a value of n for which σ (n) is a repdigit

**4443** is a number n for which n^{2}+1 is 10 times another square

**4444** is a repdigit

**4445** is the smallest number that can be written as the sum of 4 distinct positive cubes in 4 ways

**4447** is a Cuban prime

**4449** has a 4^{th} power that is the sum of four 4^{th} powers

**4455** is the number of permutations of 12 items that fix 8 elements

**4457** is the closest integer to 22^{e }

**4460** is the number of 10-ominoes without holes

**4461** is the number of asymmetrical 10-ominoes

**4465** + φ (4465) = 7777

**4467** is the number of terms in the 16^{th} derivative of f(f(f(x)))

**4473** is a value of n for which σ (n) = 2reverse(n)

**4475** = 6^{2} + 7^{3} + 8^{4}

**4480** is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

**4481** is a prime that is the average of two 4^{th} powers

**4485** is the number of 3×3 sliding puzzle positions that require exactly 16 moves to solve starting with the hole in a corner

**4488** = 256 + 257 + . . . + 272 = 273 + 274 + . . . + 288

**4489** is a square whose digits are non-decreasing

**4493** is the number of ways to divide a 11×11 grid of points into two sets using a straight line

**4495** = _{31}C _{3}

**4498** is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

**4500** is the number of regions formed when all diagonals are drawn in a regular 20-gon

**4503** is the largest number that is not the sum of 4 or fewer squares of composites

**4505** is a Zeisel number

**4506** is the sum of its proper divisors that contain the digit 5

**4510** = 4444 + 55 + 11 + 0

**4511** = 4444 + 55 + 11 + 1

**4512** = 4444 + 55 + 11 + 2

**4513** = 4444 + 55 + 11 + 3

**4514** = 4444 + 55 + 11 + 4

**4515** = 4444 + 55 + 11 + 5

**4516** = 4444 + 55 + 11 + 6

**4517** = 4444 + 55 + 11 + 7

**4518** = 4444 + 55 + 11 + 8

**4519** = 4444 + 55 + 11 + 9

**4520** is the number of regions the complex plane is cut into by drawing lines between all pairs of 20^{th} roots of unity

**4522** is the number of non-intersecting rook paths joining opposite corners of a 8×3 chessboard

**4523** has a square in base 2 that is palindromic

**4524** is the maximum number of pieces a torus can be cut into with 29 cuts

**4526** is the maximum number of regions a cube can be cut into with 30 cuts

**4527** is a value of n for which n and 7n together use each digit 1-9 exactly once

**4530** has the property that the sum of the factorials of its digits is its largest prime factor

**4535** is the number of unlabeled topologies with 7 elements

**4536** is the Stirling number of the first kind s(9,6)

**4541** has a square with the first 3 digits the same as the next 3 digits

**4542** is the number of trees on 20 vertices with diameter 5

**4544** is a Kaprekar number for cubes

**4547** is a value of n for which one more than the product of the first n primes is prime

**4548** is the sum of its proper divisors that contain the digit 7

**4550** is the Stirling number of the second kind S(15,13)

**4552** has a square with the first 3 digits the same as the next 3 digits

**4556** is the trinomial coefficient T(17,13)

**4558** is a member of the Fibonacci -type sequence starting with 1 and 4

**4562** is the number of divisors of the 17^{th} perfect number

**4563** is an Achilles number

**4565** is the number of partitions of 29

**4567** has digits in arithmetic sequence

**4576** is a truncated tetrahedral number

**4579** is an octahedral number

**4582** is the number of partitions of 52 into distinct parts

**4583** is a value of n for which one less than the product of the first n primes is prime

**4589** is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged

**4591** is a value of n for which n and 8n together use each digit 1-9 exactly once

**4600** is a decagonal pyramidal number

**4604** is a value of n for which |cos(n)| is smaller than any previous integer

**4607** is a Woodall number

**4608** is the number of ways to place 2 non-attacking kings on a 10×10 chessboard

**4609** is a Cullen number

**4610** is a Perrin number

**4613** is the number of graphs with 10 edges

**4614** is the number of ways to stack 27 pennies in contiguous rows so that each penny lies on the table or on two pennies

**4615** is a value of n for which σ (φ (n)) = 2σ (n)

**4616** has a square comprised of the digits 0-7

**4619** is a value of n for which 4n and 5n together use each digit exactly once

**4620** is the largest order of a permutation of 30 or 31 elements

**4622** is the number of 12-ominoes that contain 1 hole

**4623** is a value of n for which σ (n) = 2reverse(n)

**4624** = 4^{4} + 4^{6} + 4^{2} + 4^{4}

**4625** is the number of trees on 16 vertices with diameter 7

**4628** is a Friedman number

**4631** has a cube with only odd digits.

**4640** is the number of different score sequences of an 11-team round robin tournament]

**4641** is a rhombic dodecahedral number

**4642** is the smallest number whose cube has 11 digits

**4644** is a value of n for which 7n and 9n together use each digit exactly once

**4645** has the property that the concatenation of its prime factors in increasing order is a square

**4647** is a member of the Fibonacci -type sequence starting with 1 and 7

**4649** has a 9^{th} root that starts 2.55555...

**4650** is the maximum number of regions space can be divided into by 25 spheres

**4652** is the number of labeled connected graphs with 6 vertices that have chromatic number 4

**4653** is a value of n for which n and 6n together use each digit 1-9 exactly once

**4655** is the number of 10-ominoes

**4657** is a number that does not have any digits in common with its cube

**4662** is the number of ways to place 2 non-attacking knights on a 10×10 chessboard

**4663** is the number of 12-ominoes that contain holes

**4665** = 33333 in base 6

**4666** is the number of tilted rectangles with vertices in a 13×13 grid

**4672** is a permutation of the sum of its proper divisors

**4675** 2^{4} + 3^{4} + 4^{4} + 5^{4} + 6^{4} + 7^{4}

**4676** is the sum of the first seven 4^{th} powers

**4680** is a value of n for which n, n^{2}, and n^{3} have the same digit sum

**4681** = 11111 in base 8

**4682** is the number of subsets of {1,2,3,...,16} that have a sum divisible by 14

**4683** is the number of orderings of 6 objects with ties allowed (A000670)

**4684** is the number of subsets of {1,2,3,...,15} that have a sum divisible by 7

**4685** is the number of anisohedral 15-hexes

**4686** is the denominator of the 70^{th} Bernoulli number

**4687** is a value of n for which σ (φ (n)) = 3σ (n)

**4688** is 2-automorphic

**4689** is a value of n for which n and 8n together use each digit 1-9 exactly once

**4691** is a value of n for which n and 8n together use each digit 1-9 exactly once

**4695** are the first 4 digits of 4^{4695}

**4697** is a value of n for which φ (n) = φ (reverse(n))

**4698** is the smallest number so that it and its reverse are divisible by 54

**4705** is the sum of consecutive squares in 2 ways

**4709** is the number of symmetric plane partitions of 31

**4713** is a value of n such that the n^{th} Cullen number is prime

**4714** is the smallest number whose square begins with four 2's

**4723** is the index of a prime Fibonacci number

**4725** is an odd abundant number (A005101, A005231)

**4726** is the smallest number whose cube contains 5 consecutive 5's

**4727** is the sum of the squares . of the first 12 primes

**4730** is the number of multigraphs with 5 vertices and 13 edges

**4732** is a number that does not have any digits in common with its cube

**4734** is the sum of its proper divisors that contain the digit 7

**4735** is a value of n for which 4n and 5n together use each digit exactly once

**4738** is a Menage number

**4740** is the trinomial coefficient T(10,3)

**4741** is a value of n for which 4n and 5n together use each digit exactly once

**4743** is a value of n for which 2n and 5n together use the digits 1-9 exactly once

**4748** is a value of n for which σ (n) = φ (n) + φ (n-1) + φ (n-2)

**4750** is a hexagonal pyramidal number

**4751** is the starting location of 8888 in the decimal expansion of π

**4752** = (4+4) × (4+7) × (4+5) × (4+2)

**4755** has a cube whose digits occur with the same frequency

**4757** is the number of ordered partitions of 23 into distinct parts

**4758** does not occur in its factorial in base 2

**4760** is the sum of consecutive squares in 2 ways

**4761** is the number of subsets of {1,2,3,...,15} that have an integer average

**4762** is the smallest number not a power of 10 whose square contains the same digits

**4764** is an hexagonal prism number

**4766** is the number of rooted trees with 12 vertices (A000081)

**4769** is a value of n for which 4n and 5n together use each digit exactly once

**4776** is a structured pentagonal hexacontahedral number

**4780** has a square whose digits each occur twice

**4784** has a sum of digits equal to its largest prime factor

**4785** has a square that is the sum of a cube and a 4^{th} power

**4787** is a value of n for which one more than the product of the first n primes is prime

**4788** is a Keith number

**4793** = 4444 + 7 + 9 + 333

**4797** is a cubic star number

**4798** is a value of n for which n!!! + 1 is prime

**4801** is a number n for which n^{2}+1 is 6 times another square

**4802** can be written as the sum of 2 or 3 positive 4^{th} powers

**4804** is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals .

**4807** is the smallest quasi-Carmichael number in base 10

**4815** is the number of ways to stack 33 boxes in a line so that each box lies on the table or on a box next to 2 boxes

**4819** is a Tetranacci -like number starting from 1, 1, 1, and 1

**4823** is the number of triangles of any size contained in the triangle of side 26 on a triangular grid

**4831** is the smallest prime so that it and the next 2 primes all end in 1

**4832** is a number whose square contains the same digits

**4835** is the number of anisohedral 14-hexes

**4843** is a value of n for which σ (φ (n)) = 2σ (n)

**4845** = _{20}C _{4}

**4848** is the number of quaternary square-free words of length 8

**4850** is a Wedderburn-Etherington number

**4851** is a pentagonal pyramidal number

**4852** is the sum of the squares of 4 consecutive primes

**4854** does not occur in its factorial in base 2

**4860** is the order of a perfect group

**4862** is the 9^{th} Catalan number

**4863** is the smallest number that cannot be written as the sum of 273 8^{th} powers

**4866** is the number of partitions of 48 in which no part occurs only once

**4869** is a value of n for which 3n and 8n together use each digit exactly once

**4875** is the number of graphs with 10 vertices and 3 cycles

**4876** divides the sum of the first 681 composite numbers

**4877** is the largest prime factor of 87654321

**4878** is the number of alternating knots with 13 crossings

**4879** = 238 + 0 + 4641 and has the square 23804641

**4889** 2^{6} + 3^{6} + 4^{6}

**4890** is a narcissistic number in base 5

**4891** is a narcissistic number in base 5

**4893** is a value of n for which 2n and 7n together use the digits 1-9 exactly once

**4895** is the product of two consecutive Fibonacci numbers

**4896** = _{18}P _{3}

**4899** is the sum of the squares of 3 consecutive primes

**4900** is the only non-trivial number which is both square and square pyramidal

**4901** has a base 3 representation that begins with its base 7 representation

**4902** is the starting location of 2222 in the decimal expansion of π

**4905** is the sum of all the 2-digit numbers

**4911** has a 9^{th} power whose first few digits are 16616111...

**4913** is the cube of the sum of its digits

**4917** is the trinomial coefficient T(11,5)

**4919** is a prime that remains prime if any digit is deleted

**4920** = 6666 in base 9

**4922** is a number whose sum of divisors is a 5^{th} power

**4923** and the two numbers before it and after it are all products of exactly 3 primes

**4924** and the two numbers before it and after it are all products of exactly 3 primes

**4927** is a value of n for which 4n and 5n together use each digit exactly once

**4928** is a structured truncated tetrahedral number

**4930** = 6677_{9} = 2A2A_{12} = 2323_{13} = 1010_{17}, each using two digits exactly twice each

**4931** is a value of n for which 2n and 7n together use the digits 1-9 exactly once

**4933** is the number of digits in the 14^{th} Fermat number

**4936** = 4 + 44 + 444 + 4444

**4939** has the property that the concatenation of its prime factors in increasing order is a square

**4941** is a centered cube number

**4944** is a value of n for which n φ (n) is a palindrome

**4949** has a 4^{th} power that is the sum of four 4^{th} powers

**4950** is both a triangular number and 5 times a triangular number

**4952** is the closest integer to 15^{π }

**4959** is a value of n for which |cos(n)| is smaller than any previous integer

**4960** = _{32}C _{3}

**4961** is a Hexanacci -like number starting from 1, 1, 1, 1, 1, and 1

**4964** is the number of binary partitions of 42

**4967** is the number of partitions of 49 in which no part occurs only once

**4974** is the sum of its proper divisors that contain the digit 8

**4975** is a value of n for which n!!! + 1 is prime

**4979** is a centered tetrahedral number

**4980** has the same digits as the 4980^{th} prime

**4982** is a number whose sum of divisors is a 5^{th} power

**4985** is the number of graphs with 8 vertices with clique number 4

**4988** is the smallest multiple of 29 whose digits add to 29

**4990** is the maximum number of pieces a torus can be cut into with 30 cuts

**4991** is a Lucas-Carmichael number (A006972)

**4992** is the maximum number of regions a cube can be cut into with 31 cuts

**4993** is a Proth prime

**4995** has a 5^{th} power that is closer to a cube than a square

**4999** is the smallest number whose digits add to 31