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# Annotated version of "What's Special About This Number?" (Part 2)

## 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.

To add a link to sequence A000108, for example, type A000108.

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 2: The Numbers 2000 to 2999

**2000** = 5555 in base 7

**2001** has a square with the first 3 digits the same as the next 3 digits

**2002** = binomial(14,5)

**2003** is a Lucas 8-step number

**2004** has a square with the last 3 digits the same as the 3 digits before that

**2007** divides the sum of the digits of 2^{2007} × 2007!

**2008** is a Kaprekar constant in base 3

**2009** ! ends in exactly 500 zeros

**2010** is the number of trees on 15 vertices with diameter 7

**2015** is a Lucas-Carmichael number (A006972)

**2016** is a value of n for which n^{2} + n^{3} contains one of each digit

**2017** is a value of n for which φ (n) = φ (n-1) + φ (n-2)

**2020** is an autobiographical number

**2021** is the product of two consecutive primes

**2024** = _{24}C _{3}

**2025** is a square that remains square if all its digits are incremented

**2028** is the number of graphs with 9 vertices that have chromatic number 6

**2029** is an Eisenstein-Mersenne prime (A066408)

**2030** is the smallest number that can be written as a sum of 3 or 4 consecutive squares

**2034** is the number of self-avoiding walks of length 9

**2036** is the number of ways 11 people can line up so that only one person has a taller person in front of him

**2037** is a truncated cube number

**2038** is the number of Eulerian graphs with 9 vertices

**2039** is the smallest prime that contains ten 1's in binary

**2040** = 2040_{5} + 2040_{7} + 2040_{8}

**2041** is a 12-hyperperfect number

**2044** is the number of rectangles with corners on an 9×9 grid of points

**2045** is the number of unlabeled partially ordered sets of 7 elements

**2046** is the maximum number of pieces a torus can be cut into with 22 cuts

**2047** is the smallest composite Mersenne number with prime exponent

**2048** is the smallest non-trivial 11^{th} power

**2049** is a Cullen number

**2050** is the number of subsets of the 22^{nd} roots of unity that add to 0

**2053** is a value of n for which one less than the product of the first n primes is prime

**2054** is the number of subsets of the 33^{rd} roots of unity that add to 0

**2055** is the rectilinear crossing number of complete graph K_{21}

**2056** is the magic constant of a 16×16 magic square

**2057** is a centered icosahedral number

**2058** is the number of integers with complexity 27

**2059** is a centered tetrahedral number

**2061** is the number of sets of distinct positive integers with mean 7

**2063** is a member of the Fibonacci -type sequence starting with 3 and 7

**2067** is a value of n so that n(n+5) is a palindrome

**2072** is the smallest number that can be written in exactly 6 ways as the sum of a number and the product of its non-zero digits

**2073** is a Genocchi number

**2074** is the smallest number that can not be formed using the digit 1 at most 24 times, together with the symbols +, –, × and ÷

**2076** is a value of n for which n!!! + 1 is prime

**2078** has a cube whose digits occur with the same frequency

**2080** is the number of different arrangements (up to rotation and reflection) of 26 non-attacking bishops on a 14×14 chessboard

**2081** is a number n for which n, n+2, n+6, and n+8 are all prime

**2082** is the sum of its proper divisors that contain the digit 4

**2089** is the smallest number that ends an arithmetic progression of 10 numbers with the same prime signature

**2090** is the number of possible rows in a 17×17 crossword puzzle

**2100** is divisible by its reverse

**2101** = 2101_{5} + 2101_{7} + 2101_{8}

**2108** does not occur in its factorial in base 2

**2109** is a value of n so that n(n+7) is a palindrome

**2110** is a value of n for which reverse(φ (n)) = φ (reverse(n))

**2112** is the number of subsets of {1, 1/2, 1/3, ... 1/36} that sum to an integer

**2113** is a Proth prime

**2114** is a number whose product of digits is equal to its sum of digits

**2116** has a base 10 representation which is the reverse of its base 7 representation

**2118** is a member of the Fibonacci -type sequence starting with 1 and 5

**2119** is a value of n for which |cos(n)| is smaller than any previous integer

**2120** is the number of ways to stack 16 pennies in a line so that each penny lies on the table or on two pennies

**2122** is the index of a prime Euclid number

**2126** is a value of n so that n(n+3) is a palindrome

**2127** is not the sum of a square , a cube , a 4^{th} power, and a 5^{th} power

**2128** is the 7^{th} central quadrinomial coefficient

**2130** and its reverse are both the averages of twin primes

**2131** is the number of domino tilings of a 3×12 rectangle

**2132** is the maximum number of 11^{th} powers needed to sum to any number

**2133** is a 2-hyperperfect number

**2135** is a value of n for which σ (n-1) + σ (n+1) = σ (2n)

**2137** does not occur in its factorial in base 2

**2138** does not occur in its factorial in base 2

**2140** is a cubic star number

**2141** is a number whose product of digits is equal to its sum of digits

**2143** is the number of commutative semigroups of order 6

**2146** is a value of n for which 2φ (n) = φ (n+1)

**2147** has a square with the last 3 digits the same as the 3 digits before that

**2148** is the number of 15-ominoes with a horizontal or vertical line of symmetry

**2150** divides the sum of the largest prime factors of the first 2150 positive integers

**2155** is the smallest number whose cube has 10 digits

**2156** is the number of different positions in Connect Four after 5 moves

**2158** is a number n for which n^{2}+1 is 6 times another square

**2160** is the order of a perfect group (A060793)

**2161** is a prime factor of 111111111111111111111111111111

**2163** are the first 4 digits of π ^{2163}

**2164** is the smallest number whose 7^{th} power starts with 5 identical digits

**2168** is a structured hexagonal diamond number

**2169** is a Leyland number

**2176** is the number of prime knots with 12 crossings

**2178** is the only number known which when multiplied by its reverse yields a 4^{th} power

**2179** is a Wedderburn-Etherington number (A001190)

**2182** is the number of degree 15 irreducible polynomials over GF(2)

**2184** is the product of three consecutive Fibonacci numbers

**2185** is the number of digits of 5^{55}

**2186** = 2222222 in base 3

**2187** is a strong Friedman number

**2188** is the 10^{th} Motzkin number

**2192** is the number of necklaces (that can't be turned over) possible with 15 beads, each being one of 2 colors

**2194** is the number of partitions of 42 in which no part occurs only once

**2195** is the number of necklaces with 9 beads, each one of 3 colors

**2196** is the only number n so that 2n, 3n, 7n, and 9n together contain every digit 1-9 exactly twice

**2197** = 13^{3}

**2199** is a perfect totient number

**2201** is the only non-palindrome known to have a palindromic cube

**2202** is a factor of the sum of the digits of 2202^{2202}

**2203** is the exponent of a Mersenne prime (A000043, A000668)

**2204** has the property that the sum of the factorials of its digits is its largest prime factor

**2205** is an odd primitive abundant number (A091191, A006038)

**2207** is the 16^{th} Lucas number

**2208** is a Keith number

**2209** is a Tribonacci -like number starting from 1, 1, and 1

**2210** = _{47}C _{2} + _{47}C _{2} + _{47}C _{1} + _{47}C _{0}

**2211** is a triangular number whose internal digits are triangular and whose external digits are triangular

**2212** is the closest integer to 17^{e }

**2213** = 2^{3} + 2^{3} + 13^{3}

**2217** has a base 2 representation that begins with its base 3 representation

**2219** is the number of 14-hexes with reflectional symmetry

**2221** is a value of n for which σ (n) is a repdigit

**2222** is the smallest number divisible by a 1-digit prime , a 2-digit prime , and a 3-digit prime

**2223** is a Kaprekar number (A006886)

**2225** has the property that the sum of the n^{th} powers of its digits is prime for 1 ≤ n &\le 9

**2226** is the smallest number whose cube contains 4 consecutive 9's

**2234** is the number of ways to stack 24 pennies in contiguous rows so that each penny lies on the table or on two pennies

**2235** is a value of n so that n(n+8) is a palindrome

**2239** is a prime that remains prime if any digit is deleted

**2240** is the number of unsymmetrical ways to dissect a regular 13-gon into 11 triangles

**2241** is the sum of 3 consecutive cubes

**2243** is the smallest prime so that it and the next 2 primes are all equal to 3 (mod 8)

**2244** is the generalized Catalan number C(14,4)

**2245** is the number of ways to tile a 8×4 rectangle with 2×1 rectangles

**2250** is the number of necklaces possible with 16 beads, each being one of 2 colors

**2252** is a Franel number

**2253** is the number of monic polynomials of degree 11 with integer coefficients whose complex roots are all in the unit disk

**2255** is the number of triangles of any size contained in the triangle of side 20 on a triangular grid

**2257** = 4321 in base 8

**2258** is the number of anisohedral 16-ominoes

**2260** is an icosahedral number

**2261** = 2222 + 22 + 6 + 11

**2263** = 2222 + 2 + 6 + 33

**2264** is the number of graphs with 8 vertices that have 4 automorphisms

**2266** is a dodecagonal pyramidal number

**2268** is the number of binary partitions of 34

**2269** is a Cuban prime

**2272** is the number of graphs on 7 vertices with no isolated vertices

**2273** is the number of functional graphs on 10 vertices

**2274** is the sum of its proper divisors that contain the digit 7

**2275** is the sum of the first six 4^{th} powers

**2277** is the trinomial coefficient T(11,6)

**2281** is the exponent of a Mersenne prime (A000043, A000668)

**2282** is the number of ways, up to rotation and reflection, of dissecting a regular 13-gon into 11 triangles

**2284** is the number of 7-digit perfect powers

**2285** is a non-palindrome with a palindromic square

**2291** is the number of inequivalent Ferrers graphs with 29 points

**2292** is a narcissistic number in base 6

**2293** is a prime that remains prime if any digit is deleted

**2295** is the smallest number so that it and its successor are both the product of 2 primes and the cube of a prime

**2296** is a structured great rhombicubeoctahedral number

**2297** is the number of inequivalent binary linear codes of length 10

**2299** is the number of ordered sequences of coins totaling 28 cents

**2300** = _{25}C _{3}

**2303** is a number whose square and cube use different digits

**2304** is the number of edges in a 9 dimensional hypercube

**2305** has a base 6 representation that ends with its base 8 representation

**2306** has a base 6 representation that ends with its base 8 representation

**2307** has a base 6 representation that ends with its base 8 representation

**2308** is the number of conjugacy classes of the alternating group A_{29}

**2309** is the largest prime factor of 2 × 3 × 5 × 7 × 11 - 1

**2310** is the product of the first 5 primes

**2311** is a Euclid number

**2312** is the number of series-reduced planted trees with 10 leaves

**2316** = 1^{7} + 2^{7} + 3^{7}

**2318** is the number of connected planar graphs with 10 edges

**2320** is the maximum number of regions space can be divided into by 20 spheres

**2321** is a Huay rhombic dodecahedral number

**2322** is the number of connected graphs with 10 edges

**2323** is the maximum number of pieces a torus can be cut into with 23 cuts

**2324** is a narcissistic number in base 6

**2325** is the maximum number of regions a cube can be cut into with 24 cuts

**2326** is the smallest number whose cube contains every digit at least once

**2328** is the number of groups of order 128

**2331** is a centered cube number

**2333** is a right-truncatable prime

**2336** is the number of sided 11-iamonds

**2339** is the number of ways to tile a 6×10 rectangle with the pentominoes

**2340** = 4444 in base 8

**2342** is the number of subsets of {1,2,3,...,15} that have a sum divisible by 14

**2343** = 33333 in base 5

**2344** is the number of necklaces with 7 beads, each one of 4 colors

**2345** has digits in arithmetic sequence

**2349** is a Friedman number

**2350** is the number of quasi-triominoes that fit inside a 11×11 grid

**2351** is a member of the Fibonacci -type sequence starting with 2 and 5

**2352** does not occur in its factorial in base 2

**2353** has the property that 588^{2} + 2353^{2} = 5882353 and 9412^{2} + 2353^{2} = 94122353

**2354** = 2222 + 33 + 55 + 44

**2357** is the smallest number whose square begins with four 5's

**2359** = 2222 + 33 + 5 + 99

**2360** is a hexagonal pyramidal number

**2363** does not occur in its factorial in base 2

**2365** is a value of n for which n (n+2) is a palindrome

**2366** is the number of ways to legally add 2 sets of parentheses to a product of 12 variables

**2368** is the number of 3×3 sliding puzzle positions that require exactly 14 moves to solve starting with the hole in the center

**2371** is the number of ways a 7×1 rectangle can be surrounded by 7×1 rectangles

**2372** is the smallest number whose 8^{th} power has 27 digits

**2376** is a structured truncated tetrahedral number

**2377** is a value of n for which one less than the product of the first n primes is prime

**2378** is the 10^{th} Pell number

**2380** = _{17}C _{4}

**2385** is the smallest number whose 7^{th} power contains exactly the same digits as another 7^{th} power

**2387** is a structured rhombic triacontahedral number

**2388** is the number of 3-connected graphs with 8 vertices

**2391** is the number of ways to flip a coin 12 times and get at least 3 heads in a row

**2393** is a right-truncatable prime

**2394** is the smallest value of n for which n and 7n together use each digit 1-9 exactly once

**2397** is the number of intersections when all the diagonals of a regular 17-gon are drawn

**2398** is the number of 3×3 sliding puzzle positions that require exactly 28 moves to solve starting with the hole in the center

**2399** is a right-truncatable prime

**2400** = 6666 in base 7

**2401** is the 4^{th} power of the sum of its digits

**2402** has a base 2 representation that begins with its base 7 representation

**2405** has the property that if each digit is replaced by its square , the resulting number is a square

**2406** is a truncated octahedral number

**2407** is a value of n for which σ (φ (n)) = 2σ (n)

**2410** is the number of 3-valent trees with 16 vertices

**2411** is a number whose product of digits is equal to its sum of digits

**2414** is the number of symmetric plane partitions of 28

**2417** has a base 3 representation that begins with its base 7 representation

**2420** is the number of possible rook moves on a 11×11 chessboard

**2424** has a cube that contains the digits 2424 in reverse order

**2427** = 2^{1} + 4^{2} + 2^{3} + 7^{4}

**2430** is the number of unordered ways to write 1 as a sum of reciprocals of integers no larger than 18

**2431** is the Stirling number of the second kind S(13,11)

**2432** does not occur in its factorial in base 2

**2434** is the number of legal king moves in Chess

**2436** is the number of partitions of 26

**2445** is a truncated tetrahedral number

**2448** is the order of a non-cyclic simple group

**2450** has a base 3 representation that begins with its base 7 representation

**2457** = 169 + 170 + . . . + 182 = 183 + 184 + . . . + 195

**2460** = 3333 in base 9

**2464** is the number of permutations of 8 items that fix 3 elements

**2465** is a Carmichael number

**2466** is the number of regions formed when all diagonals are drawn in a regular 18-gon

**2467** has a square with the first 3 digits the same as the next 3 digits

**2468** = 2 + 22 + 222 + 2222

**2469** is the smallest value of n for which 4n and 5n together use the digits 1-9 exactly once

**2470** is the sum of the first 19 squares

**2471** is the smallest number that can not be formed using the numbers 2^{0}, 2^{1}, ... , 2^{6}, together with the symbols +, –, × and ÷

**2474** is a value of n for which |cos(n)| is smaller than any previous integer

**2477** would be prime if preceded and followed by a 1, 3, 7, or 9

**2478** is the number of anisohedral 20-iamonds

**2484** is the number of regions the complex plane is cut into by drawing lines between all pairs of 18^{th} roots of unity

**2485** is the number of planar partitions of 13

**2487** has a 4^{th} power that is the sum of four 4^{th} powers

**2491** is the product of two consecutive primes

**2492** is the larger number in a Ruth-Aaron pair

**2495** is the number of 13-iamonds that tile the plane

**2496** is the number of 3-connected planar maps with 17 edges

**2498** shares 3 consecutive digits with one of its prime factors

**2499** has a square root that starts 49.989998999...

**2500** is a Tetranacci -like number starting from 1, 1, 1, and 1

**2501** is a Friedman number

**2502** is a strong Friedman number

**2503** is a Friedman number

**2504** is a Friedman number

**2505** is a Friedman number

**2506** is a Friedman number

**2507** is a Friedman number

**2508** is a Friedman number

**2509** is a Friedman number

**2510** 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 10 stamps

**2511** is the smallest number so that it and its successor are both the product of a prime and the 4^{th} power of a prime

**2512** is the smallest number whose 5^{th} power has 17 digits

**2513** is a Padovan number

**2515** is the number of symmetric 9-cubes

**2517** is the number of regions the complex plane is cut into by drawing lines between all pairs of 17^{th} roots of unity

**2518** uses the same digits as φ (2518)

**2519** is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 12

**2520** is the smallest number divisible by 1 through 10

**2522** is the number of subsets of {1,2,3,...,15} that have a sum divisible by 13

**2524** and the two numbers before it and after it are all products of exactly 3 primes

**2525** and the two numbers before it and after it are all products of exactly 3 primes

**2528** is a structured truncated octahedral number

**2530** is a Leyland number

**2532** = 2222 + 55 + 33 + 222

**2535** is the number of ways to 13-color the faces of a tetrahedron

**2538** has a square with 5/7 of the digits are the same

**2540** has a square root whose decimal part starts with the digits 0-9 in some order

**2542** is the number of stretched 9-ominoes

**2545** = 2545_{6} + 2545_{9}

**2548** is the generalized Catalan number C(11,5)

**2550** is a Kaprekar constant in base 4

**2557** is the number of proper divisors of the 15^{th} perfect number

**2558** is the number of divisors of the 15^{th} perfect number

**2560** is the number of 2×2 singular matrices mod 8

**2561** is the number of digits of the 19^{th} perfect number (A061193)

**2562** is a structured pentakis dodecahedral number

**2570** is the number of subsets of {1,2,3,...,14} that have an integer average

**2571** is the smallest number with the property that its first 7 multiples contain the digit 1

**2574** is a value of n for which _{2n}C _{n} is divisible by n^{2}

**2576** has exactly the same digits in 3 different bases

**2580** is a Keith number

**2581** is the smallest number whose square begins with three 6's

**2582** is the smallest number whose square begins with four 6's

**2583** is the sum of the first 16 Fibonacci numbers

**2584** is the 18^{th} Fibonacci number

**2585** is a truncated square pyramid number

**2587** is a value of n for which φ (n) + φ (n+1) divides σ (n) + σ (n+1)

**2590** is the number of partitions of 47 into distinct parts

**2592** = 2^{5} 9^{2}

**2593** has a base 3 representation that ends with its base 6 representation

**2594** has a base 3 representation that ends with its base 6 representation

**2596** is the number of triangles of any size contained in the triangle of side 21 on a triangular grid

**2600** = _{26}C _{3}

**2601** is a pentagonal pyramidal number

**2606** is the number of polyhedra with 9 vertices

**2609** is the number of perfect squared rectangles of order 15

**2614** is the smallest value of n for which π(9n) = n

**2615** is the number of functions from 9 unlabeled points to themselves

**2616** is the number of graphs with 9 vertices and 6 cycles

**2617** is the index of a Wagstaff prime

**2618** has a sum of digits equal to its largest prime factor

**2620** is an amicable number

**2621** = 2222 + 66 + 222 + 111

**2622** is a value of n for which 7n and 8n together use each digit exactly once

**2623** = 2222 + 66 + 2 + 333

**2624** is the maximum number of pieces a torus can be cut into with 24 cuts

**2625** is a centered octahedral number

**2626** is the maximum number of regions a cube can be cut into with 25 cuts

**2627** is a Perrin number

**2629** is the smallest number whose reciprocal has period 14

**2631** is a Lucas 4-step number

**2632** has the same digits as the 2632^{nd} prime

**2635** is the number of necklaces with 6 beads, each one of 5 colors

**2636** is a non-palindrome with a palindromic square

**2637** is the number of commutative monoids of order 7

**2639** is an enneagonal pyramidal number

**2641** is the pseudosquare modulo 11

**2642** = 5^{2} + 6^{3} + 7^{4}

**2646** is the Stirling number of the second kind S(9,6)

**2647** is the index of a prime Euclid number

**2651** is the number of asymmetric trees with 12 vertices

**2652** is the 9^{th} super-ballot number

**2657** is a value of n for which one more than the product of the first n primes is prime

**2659** 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 13 stamps

**2662** is a palindrome and the 2662^{nd} triangular number is a palindrome

**2663** is the number of digits of the 20^{th} perfect number (A061193)

**2664** is the smallest value of n for which n, n+1, n+2, n+3, and n+4 have the same number of prime factors

**2665** is the number of conjugacy classes in the automorphism group of the 14 dimensional hypercube .

**2667** is a number whose sum of divisors is a 6^{th} power

**2668** is the number of lines through exactly 2 points of a 11×11 grid of points

**2671** is a value of n for which 2n and 7n together use the digits 1-9 exactly once

**2672** and its successor are both divisible by 4^{th} powers

**2673** is the largest number known that does not have any digits in common with its 4^{th} power

**2680** is the number of different arrangements of 11 non-attacking queens on an 11×11 chessboard

**2683** is the largest n so that **Q** (√n) has class number 5

**2685** is a value of n for which σ (n) = σ (n+1)

**2688** is the order of a perfect group (A060793)

**2689** is a Proth prime

**2690** is the number of terms in the 9^{th} derivative of f(f(f(f(f(x)))))

**2692** is the sum of the squares of 4 consecutive primes

**2694** is the number of ways 22 people around a round table can shake hands in a non-crossing way, up to rotation

**2697** is the smallest value of n for which n and 5n together use each digit 1-9 exactly once

**2700** is the product of the first 5 triangular numbers

**2701** is the smallest number n which divides the average of the n^{th} prime and the primes surrounding it

**2702** is the maximum number of regions space can be divided into by 21 spheres

**2704** is the number of necklaces with 9 white and 9 black beads

**2710** is an hexagonal prism number

**2712** is the number of 12-ominoes that tile the plane by translation

**2717** is the number of 9-hexes that do not tile the plane

**2718** is the integer part of 1000e

**2722** has the property that if each digit is replaced by its square , the resulting number is a square

**2725** is the number of fixed octominoes

**2728** is a Kaprekar number (A006886)

**2729** has a square with the first 3 digits the same as the next 3 digits

**2730** = _{15}P _{3}

**2731** is a Wagstaff prime

**2733** is the number of possible positions in Checkers after 5 moves

**2736** is an octahedral number

**2737** is a strong Friedman number

**2743** is a centered dodecahedral number

**2744** is the smallest number that can be written as the sum of a cube and a 4^{th} power in more than one way

**2745** divides the sum of the primes less than it

**2749** is the smallest index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged

**2751** is the number of ordered partitions of 21 into distinct parts

**2753** is the number of subsequences of {1,2,3,...13} in which every odd number has an even neighbor

**2757** is the number of possible configurations of pegs (up to symmetry) after 7 jumps in solitaire

**2758** has the property that placing the last digit first gives 1 more than triple it

**2766** in hexadecimal spells the word ACE

**2767** is the smallest number that can not be formed using the digit 1 at most 25 times, together with the symbols +, –, × and ÷

**2768** is 7-automorphic

**2769** is a value of n for which n and 5n together use each digit 1-9 exactly once

**2770** is the Entringer number E(8,1).

**2773** is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with integer dimensions less than 12

**2780** = 1^{8} + 2^{7} + 3^{6} + 4^{5} + 5^{4} + 6^{3} + 7^{2} + 8^{1}

**2782** 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 19 stamps

**2783** is the smallest number whose 9^{th} power has 31 digits

**2786** is the 9^{th} Pell-Lucas number

**2787** is a value of n for which the first n binary digits of π form a prime

**2790** is the number of binary partitions of 36

**2791** is a Cuban prime

**2792** is the smallest number that can not be written using 13 copies of 13 and the operations +, –, ×, and ÷

**2793** is the number of inequivalent asymmetric Ferrers graphs with 30 points

**2801** = 11111 in base 7 (A023000)

**2802** is the sum of its proper divisors that contain the digit 4

**2805** is the smallest order of a cyclotomic polynomial whose factorization contains 6 as a coefficient

**2806** is the number of semigroups of order 6 with 2 idempotents

**2808** = (9 × 10 × 11 × 12 × 13) / (9 + 10 + 11 + 12 + 13)

**2810** has the property that the concatenation of its prime factors in increasing order is a square

**2811** is the number of inequivalent Ferrers graphs with 30 points

**2812** is the number of 8-pents

**2817** is a member of the Fibonacci -type sequence starting with 1 and 4

**2821** is a Carmichael number

**2824** is the smallest number whose cube contains six 2's

**2828** is a value of n so that n(n+8) is a palindrome

**2829** has a 4^{th} power that is the sum of four 4^{th} powers

**2832** is the number of ways to place 2 non-attacking bishops on a 9×9 chessboard

**2834** is a composite number n that divides the (n+1)^{st} Fibonacci number

**2835** is a Rhonda number

**2842** is the smallest number with the property that its first 4 multiples contain the digit 8

**2844** is the sum of the first 15 numbers that have digit sum 15

**2847** is a house number

**2848** is the smallest number whose square contains 4 consecutive 1's

**2849** is the largest number n known whose base 11 representation is equal to φ (n)

**2850** is the trinomial coefficient T(10,4)

**2855** is the smallest number that can not be formed using the digit 1 at most 21 times, together with the symbols +, × and ^

**2856** = 17!!!!!

**2857** is the number of partitions of 44 in which no part occurs only once

**2858** has a square with the first 3 digits the same as the next 3 digits

**2863** has a 10^{th} root whose decimal part starts with the digits 1-9 in some order

**2867** has the property that the concatenation of its prime factors in increasing order is a square

**2868** has a 4^{th} power containing only 4 different digits

**2869** is a centered icosahedral number

**2870** is the sum of the first 20 squares

**2871** is a cubic star number

**2872** is the 15^{th} Tetranacci number

**2874** is the number of multigraphs with 5 vertices and 12 edges

**2876** is the number of 8-hepts

**2878** is the number of integers with complexity 28

**2879** is the smallest number with complexity 27

**2880** = 4! × 5!

**2881** has a base 3 representation that ends with its base 6 representation

**2882** has a base 3 representation that ends with its base 6 representation

**2888** is the first of five consecutive squareful numbers

**2889** is a number n for which n^{2}+1 is 5 times another square

**2890** is the smallest number in base 9 whose square contains the same digits in the same proportion

**2893** is the number of planar 2-connected graphs with 8 vertices

**2897** is a Markov number

**2900** is the number of self-avoiding walks in a quadrant of length 10

**2907** is the trinomial coefficient T(9,1)

**2910** is the number of partitions of 48 into distinct parts

**2911** is a value of n for which σ (n-1) = σ (n+1)

**2913** is a value of n for which σ (n-1) + σ (n+1) = σ (2n)

**2914** is a value of n for which σ (n-1) = σ (n+1)

**2915** is a Lucas-Carmichael number (A006972)

**2916** is a Friedman number

**2917** is the number of digits of the 21^{st} Mersenne prime (A028335)

**2919** = (2 + 9 + 1 + 9) × (29 + 91 + 19)

**2920** is a heptagonal pyramidal number

**2922** is the sum of its proper divisors that contain the digit 4

**2924** is an amicable number

**2925** = _{27}C _{3}

**2926** has a sum of digits equal to its largest prime factor

**2928** is the number of partitions of 45 in which no part occurs only once

**2931** is the number of trees on 16 vertices with diameter 6

**2933** is a value of n for which σ (φ (n)) = 2σ (n)

**2937** is a value of n for which n and 5n together use each digit 1-9 exactly once

**2938** is the number of binary rooted trees with 17 vertices

**2939** is a right-truncatable prime

**2943** is the smallest value of n for which n and 6n together use each digit 1-9 exactly once

**2947** is the smallest number whose 5^{th} power starts with 4 identical digits

**2950** is the maximum number of pieces a torus can be cut into with 25 cuts

**2952** is the maximum number of regions a cube can be cut into with 26 cuts

**2953** is the smallest number whose cube contains six 7's

**2955** has a 5^{th} power whose digits all occur twice

**2958** is the number of multigraphs with 21 vertices and 4 edges

**2964** is a Smith brother

**2965** is a Smith brother

**2966** has the property that if each digit is replaced by its square , the resulting number is a square

**2967** is a value of n for which 5n and 7n together use each digit exactly once

**2970** is a harmonic divisor number

**2971** is the index of a prime Fibonacci number

**2973** is a value of n for which n and 5n together use each digit 1-9 exactly once

**2974** is a value of n for which σ (n) = σ (n+1)

**2978** is the number of unlabeled distributive lattices with 17 elements

**2981** is the closest integer to e ^{8}

**2982** is a value of n so that n(n+7) is a palindrome

**2984** is the number of different products of subsets of the set {1, 2, 3, ... 15}

**2988** is the number of series-reduced trees with 20 vertices

**2989** in hexadecimal spells the word BAD

**2991** uses the same digits as φ (2991)

**2992** is the closest integer to 19^{e }

**2993** is the number of digits of the 22^{nd} Mersenne prime (A028335)

**2996** is the number of terms in the 15^{th} derivative of f(f(f(x)))

**2997** = 222 + 999 + 999 + 777

**2998** is a value of n so that n(n+3) is a palindrome

**2999** = 2 + 999 + 999 + 999