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 2²⁰⁰⁷ × 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 n² + n³ 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 = ₂₄C 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 = 2040₅ + 2040₇ + 2040₈

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 K₂₁

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 = 2101₅ + 2101₇ + 2101₈

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 n²+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 5⁵⁵

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 = 13³

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 2202²²⁰²

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 = ₄₇C ₂ + ₄₇C ₂ + ₄₇C ₁ + ₄₇C 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 = 2³ + 2³ + 13³

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 = ₂₅C 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 A₂₉

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 = 1⁷ + 2⁷ + 3⁷

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 588² + 2353² = 5882353 and 9412² + 2353² = 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 = ₁₇C 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 = 2¹ + 4² + 2³ + 7⁴

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 2⁰, 2¹, ... , 2⁶, 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 = 2545₆ + 2545₉

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 _2nC _n is divisible by n²

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 = 2⁵ 9²

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 = ₂₆C 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 = 5² + 6³ + 7⁴

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 = ₁₅P 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 = 1⁸ + 2⁷ + 3⁶ + 4⁵ + 5⁴ + 6³ + 7² + 8¹

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 n²+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 = ₂₇C 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