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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 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 11th power
2049 is a Cullen number
2050 is the number of subsets of the 22nd 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 33rd 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 4th power, and a 5th power
2128 is the 7th 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 11th 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 7th 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 4th 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 10th 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 16th 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 17e
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 nth 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 4th 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 8th 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 10th Pell number
2380 = 17C 4
2385 is the smallest number whose 7th power contains exactly the same digits as another 7th 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 4th 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 18th roots of unity
2485 is the number of planar partitions of 13
2487 has a 4th power that is the sum of four 4th 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 4th power of a prime
2512 is the smallest number whose 5th 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 17th 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 15th perfect number
2558 is the number of divisors of the 15th perfect number
2560 is the number of 2×2 singular matrices mod 8
2561 is the number of digits of the 19th 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 18th 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 2632nd 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 9th 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 2662nd triangular number is a palindrome
2663 is the number of digits of the 20th 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 6th 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 4th powers
2673 is the largest number known that does not have any digits in common with its 4th 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 9th 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 nth 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 4th 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 9th power has 31 digits
2786 is the 9th 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 4th power that is the sum of four 4th 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 10th 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 4th 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 15th 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 21st 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 5th 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 5th 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 19e
2993 is the number of digits of the 22nd Mersenne prime (A028335)
2996 is the number of terms in the 15th 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