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

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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:

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 = 14C 4 + 14C 0 + 14C 0 + 14C 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 = 30C 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 = 17P 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 4th powers. It is also the largest number of the form 2k−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 4th powers

4098 is the number of subsets of the 26th 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 4119th prime is a palindrome .

4120 has a cube with a digit sum larger than its 7th 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 8th Bell number

4141 = 41415 + 41417 + 41418

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 = 45 + 15 + 55 + 05

4151 = 45 + 15 + 55 + 15

4152 = 45 + 15 + 55 + 2

4153 = 45 + 15 + 55 + 3

4154 = 45 + 15 + 55 + 4

4155 = 45 + 15 + 55 + 5

4156 = 45 + 15 + 55 + 6

4157 = 45 + 15 + 55 + 7

4158 = 45 + 15 + 55 + 8

4159 = 45 + 15 + 55 + 9

4160 = 43 + 163 + 03

4161 = 43 + 163 + 13

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 8th 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 = 42025 + 42027 + 42028

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 A32


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 8th 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 12th 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 4th power that is the sum of four 4th 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 18th 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 4th power that is the sum of four 4th 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 2nC n is divisible by n2

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-2k is a pseudoprime for all k>0

4312 is the smallest number whose 10th 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 4th power that is the sum of four 4th 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 4th 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 = 24 + 35 + 46

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 = 16C 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 4th 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 11 + 22 + 33 + . . . + 43884388


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 16th 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 25 + 35 + 45 + 55

4425 is the sum of the first five 5th powers


4430 is the rectilinear crossing number of complete graph K25

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 n2+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 4th power that is the sum of four 4th powers

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


4457 is the closest integer to 22e

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 16th derivative of f(f(f(x)))


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

4475 = 62 + 73 + 84

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 4th 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 = 31C 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 20th 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 17th 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 = 44 + 46 + 42 + 44

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 9th 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 24 + 34 + 44 + 54 + 64 + 74

4676 is the sum of the first seven 4th powers


4680 is a value of n for which n, n2, and n3 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 70th 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 44695

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 nth 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 4th 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 n2+1 is 6 times another square


4802 can be written as the sum of 2 or 3 positive 4th 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 = 20C 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 9th Catalan number

4863 is the smallest number that cannot be written as the sum of 273 8th 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 26 + 36 + 46

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 = 18P 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 9th 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 5th 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 = 66779 = 2A2A12 = 232313 = 101017, 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 14th 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 4th power that is the sum of four 4th powers

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

4952 is the closest integer to 15π


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

4960 = 32C 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 4980th prime

4982 is a number whose sum of divisors is a 5th 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 5th power that is closer to a cube than a square

4999 is the smallest number whose digits add to 31