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2000 (number)

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(Redirected from2459 (number))

"2,000" redirects here. For other uses, see2000 (disambiguation).

Selected numbers in the range 2001–2999

[edit]

2001 to 2099

[edit]

2001 –sphenic number^[4]
2002 = 7⁴ – 7³ – 7² – 7.Palindromic number indecimal, base 76, 90, 142, and 11 other non-trivial bases.
2003 –Sophie Germain prime and the smallest prime number in the 2000s
2004 – Area of the 24thcrystagon^[5]
2005 – A vertically symmetric number
2006 – number of subsets of {1,2,3,4,5,6,7,8,9,10,11} with relatively prime elements^[6]
2007 – 2²⁰⁰⁷ + 2007² is prime^[7]
2008 – number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to 3^[8]
2009 = 28² + 35², sum of two squares
2010 – number of compositions of 12 into relatively prime parts^[9]
2011 –sexy prime with 2017, sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211
2012 – The number 8 × 10²⁰¹² − 1 is a prime number^[10]
2013 –number of widely totally strongly normal compositions of 17
2014 – 5 × 2²⁰¹⁴ - 1 is prime^[11]
2015 –Lucas–Carmichael number^[12]
2016 –triangular number, number of 5-cubes in a 9-cube,Erdős–Nicolas number,^[13] 2¹¹-2⁵
2017 –Mertens function zero,sexy prime with 2011
2018 –Number of partitions of 60 into prime parts
2019 – smallest number that can be represented as the sum of 3 prime squares 6 different ways: 2019 = 7² + 11² + 43² = 7² + 17² + 41² = 13² + 13² + 41² = 11² + 23² + 37² = 17² + 19² + 37² = 23² + 23² + 31²^[14]
2020 – sum of thetotient function for the first 81 integers
2021 = 43 × 47, consecutiveprime numbers, next is 2491
2022 – non-isomorphic colorings of a toroidal 3 × 3 grid using exactly three colors under translational symmetry,^[15] beginning of a run of 4 consecutive Niven numbers^[16]
2023 = 7 × 17² – multiple of 7 with digit sum equal to 7,^[17] sum of squares of digits equals 17
2024 –tetrahedral number^[18]
2025 = 45², square of the sum of the first nine positive integers (and therefore sum of the cubes of the first nine positive integers, byNicomachus's theorem),centered octagonal number,^[19] lowest number with exactly 15odd divisors.^[20] Sum of odd numbers from 1 to 89, current year.
2026 = Number of hyperforests spanning 10 unlabeled nodes without isolated vertices^[21]
2027 –super-prime,safe prime^[22]
2028 = 13³ – 13²
2029 – member of theMian–Chowla sequence^[23]
2030 = 21² + 22² + 23² + 24² = 25² + 26² + 27²
2031 –centered pentagonal number^[24]
2032 – number of binary Lyndon words of length 16 with an even number of 1's^[25]
2033 – number of rooted trees with 9 nodes and a single labeled node^[26]
2034 – number of unlabeled graphs on 11 nodes whose components are unicyclic graphs^[27]
2035 – Wolstenholme number^[28]
2036 – Eulerian number^[29]
2037 = 2¹¹ - 11^[30]
2038 – Number of unlabeled Euler graphs with 9 nodes^[31]
2039 –Sophie Germain prime,safe prime^[22]
2040 = ${\frac {15\times 16\times 17}{2}}$ ^[32]
2041 – Number of 11-node connected graphs with at most one cycle^[33]
2042 = 2 × 1021. All the digits of all the prime factors are smaller than 3^[34]
2043 – Number of partitions of 35 in which the number of parts divides 35^[35]
2044 = $\sigma _{3}(12)=\sum _{d|12}d^{3}$ ^[36]
2045 – Number ofpartially ordered set with 7 unlabeled elements^[37]
2046 = 2¹¹ - 2 = the expected number of tosses of a fair coin to get 10 consecutive heads^[38]
2047 –super-Poulet number,^[39]Woodall number,^[40]decagonal number,^[41] acentered octahedral number,^[42] 2047 = 2¹¹ - 1 = 23 × 89 and is the firstMersenne number that is composite for a prime exponent
2048 =2¹¹
2049 = 2¹¹ + 2⁰. A sum of two positivepowers of two^[43]
2050 = 31² + 33². Sum of 2 consecutive odd squares
2051 = 1⁵ + 1⁵ + 1⁵ + 4⁵ + 4⁵. Sum of 5 positive 5th powers^[44]
2052 = 2¹¹ + 2². A sum of two positivepowers of two
2053 –star number
2054 = 1⁹ + 1⁹ + 1⁹ + 1⁹ + 1⁹ + 1⁹ + 2⁹ + 2⁹ + 2⁹ + 2⁹. Sum of 10 positive 9th powers
2055 = 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 2¹⁰ + 2¹⁰. Sum of 9 positive 10th powers
2056 –magic constant ofn ×n normalmagic square andn-queens problem forn = 16
2057 = 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 1¹⁰ + 2¹⁰ + 2¹⁰. Sum of 11 positive 10th powers
2058 = $49\times \phi (49)$ ^[45]
2059 = 3⁷-2⁷^[46]
2060 – sum of thetotient function for the first 82 integers
2061 – Number of sets of positive integers with arithmetic mean 7^[47]
2062 = $\phi (\phi (2062)+\sigma (2062))$ ^[48]
2063 –Sophie Germain prime,safe prime,^[22]super-prime
2064 = 1031 + 1033, which is a twin prime sum^[49]
2065 = Number of distinct lines through the origin in the fourdimensional lattice of side length 6^[50]
2066 – Bell number^[51]
2067 = Number of Golomb partitions of 30^[52]
2068 – number of 16-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed^[53]
2069 –Sophie Germain prime
2070 –pronic number^[54]
2071 = Number of sensed planar maps with 6 edges^[55]
2072 = 45² + 45 + 2^[56]
2073 – Genocchi number^[57]
2074 = Number of Baxter permutations of length 7^[58]
2075 = 411 + 413 + 415 + 417 + 419 = 25 + 50×41^[59]
2076 = Number of disconnected regular graphs with 17 nodes^[60]
2077 = Number of canonical polygons with 16 edges having 2-fold rotational symmetry^[61]
2078 = Number of reversible strings with 12 beads using exactly two different colors^[62]
2079 = ${\frac {9\cdot 10\cdot 11\cdot 12\cdot (2\cdot 9+3)}{5!}}$ , 5-dimensional pyramidal number^[63]
2080 – triangular number
2081 –super-prime
2093 – Mertens function zero
2095 – Mertens function zero
2096 – Mertens function zero
2097 – Mertens function zero
2099 – Mertens function zero,super-prime,safe prime,^[22]highly cototient number^[64]

2100 to 2199

[edit]

2100 – Mertens function zero
2101 –centered heptagonal number^[65]
2107 – member of aRuth–Aaron pair with 2108 (first definition)
2108 – member of a Ruth–Aaron pair with 2107 (first definition)
2109 –square pyramidal number,^[66] the sum of the third and last trio of three-digitpermutable primes indecimal:199 +919 +991
2112 – The break-throughalbum of the bandRush
2113 – Mertens function zero,Proth prime,^[67]centered square number^[68]
2116 = 46²
2117 – Mertens function zero
2119 – Mertens function zero
2120 – Mertens function zero, Fine number^[69]
2122 – Mertens function zero
2125 –nonagonal number^[70]
2127 – sum of the first 34 primes
2129 –Sophie Germain prime
2135 – Mertens function zero
2136 – Mertens function zero
2137 – prime of the form 2p-1
2138 – Mertens function zero
2141 –Sophie Germain prime
2142 – sum of the totient function for the first 83 integers
2143 – almost exactly 22π⁴
2145 – triangular number
2153 – with 2161, smallest consecutive primes that have the same sum of digits as each other's prime indices
2160 – largely composite number^[71]
2161 – with 2153, smallest consecutive primes that have the same sum of digits as each other's prime indices
2162 – pronic number^[54]
2166 – sum of the totient function for the first 84 integers
2169 –Leyland number^[72]
2171 – Mertens function zero
2172 – Mertens function zero
2175 – smallest number requiring 143 seventh powers for Waring representation
2176 –pentagonal pyramidal number,^[73] centered pentagonal number,^[24] number ofprime knots with 12 crossings
2178 – first natural number whose digits in its decimal representation get reversed when multiplied by 4^[74]
2179 –Wedderburn–Etherington prime^[75]
2184 – equals both 3⁷ − 3 and 13³ − 13 and is believed to be the only suchdoubly strictly absurd number^[76]^{[unreliable source?]}
2187 =3⁷,vampire number,^[77]perfect totient number^[78]
2188 –Motzkin number^[79]
2197 = 13³, palindromic in base 12 (1331₁₂)
2199 – perfect totient number^[78]

2200 to 2299

[edit]

2201 – only known non-palindromic number whosecube ispalindromic; also no known fourth or higher powers are palindromic for non-palindromic numbers
2203 – Mersenne prime exponent
2205 – oddabundant number^[80]
2207 –safe prime,^[22]Lucas prime^[81]
2208 –Keith number^[82]
2209 = 47², palindromic in base 14 (B3B₁₄), centered octagonal number^[19]
2211 – triangular number
2221 –super-prime,happy number
2222 –repdigit
2223 –Kaprekar number^[83]
2230 – sum of the totient function for the first 85 integers
2232 – decagonal number^[41]
2236 – Harshad number
2245 – centered square number^[68]
2248 – 2¹¹ + 200
2254 – member of the Mian–Chowla sequence^[23]
2255 –octahedral number^[84]
2256 – pronic number^[54]
2269 –super-prime,cuban prime^[85]
2272 – sum of the totient function for the first 86 integers
2273 –Sophie Germain prime
2276 – sum of the first 35 primes, centered heptagonal number^[65]
2278 – triangular number
2281 –star number,Mersenne prime exponent
2287 –balanced prime^[86]
2294 – Mertens function zero
2295 – Mertens function zero
2296 – Mertens function zero
2299 – member of a Ruth–Aaron pair with 2300 (first definition)

2300 to 2399

[edit]

2300 – tetrahedral number,^[18] member of a Ruth–Aaron pair with 2299 (first definition)
2301 – nonagonal number^[70]
2304 = 48²
2306 – Mertens function zero
2309 –primorial prime,twin prime with 2311, Mertens function zero, highly cototient number^[64]
2310 – fifthprimorial^[87]
2311 – primorial prime, twin prime with 2309
2321 – Mertens function zero
2322 – Mertens function zero
2326 – centered pentagonal number^[24]
2328 – sum of the totient function for the first 87 integers, the number of groups of order 128^[88]
2331 –centered cube number^[89]
2338 – Mertens function zero
2339 –Sophie Germain prime, twin prime with 2341
2341 –super-prime, twin prime with 2339
2346 – triangular number
2347 – sum of seven consecutive primes (313 + 317 + 331 + 337 + 347 + 349 + 353)
2351 –Sophie Germain prime,super-prime
2352 – pronic number^[54]
2357 –Smarandache–Wellin prime^[90]
2368 – sum of the totient function for the first 88 integers
2372 – logarithmic number^[91]
2378 –Pell number^[92]
2379 – member of the Mian–Chowla sequence^[23]
2381 –super-prime, centered square number^[68]
2393 –Sophie Germain prime
2397 – sum of the squares of the first ten primes
2399 –Sophie Germain prime

2400 to 2499

[edit]

2400 – perfect score onSAT tests administered after 2005
2401 = 49² = 7⁴, centered octagonal number^[19]
2415 – triangular number
2417 –super-prime, balanced prime^[86]
2425 – decagonal number^[41]
2427 – sum of the first 36 primes
2431 – product of three consecutive primes
2437 – cuban prime,^[85] largestright-truncatable prime in base 5
2447 –safe prime^[22]
2450 – pronic number^[54]
2456 – sum of the totient function for the first 89 integers
2458 – centered heptagonal number^[65]
2459 –Sophie Germain prime,safe prime^[22]
2465 –magic constant ofn ×n normalmagic square andn-queens problem forn = 17,Carmichael number^[93]
2470 – square pyramidal number^[66]
2471 – number of ways to partition {1,2,3,4,5,6} and then partition each cell (block) into subcells^[94]
2477 –super-prime,cousin prime
2480 – sum of the totient function for the first 90 integers
2481 – centered pentagonal number^[24]
2484 – nonagonal number^[70]
2485 – triangular number, number of planar partitions of 13^[95]
2491 = 47 * 53, consecutiveprime numbers, member ofRuth–Aaron pair with 2492 under second definition
2492 – member of Ruth–Aaron pair with 2491 under second definition

2500 to 2599

[edit]

2500 = 50²,palindromic in base 7 (10201₇)
2501 – Mertens function zero
2502 – Mertens function zero
2503 – Friedman prime
2510 – member of the Mian–Chowla sequence^[23]
2513 – member of thePadovan sequence^[96]
2517 – Mertens function zero
2519 – the smallest number congruent to 1 (mod 2), 2 (mod 3), 3 (mod 4), ..., 9 (mod 10)
2520 –superior highly composite number; smallest number divisible by numbers1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 12;colossally abundant number;Harshad number in several bases. It is also the highest number with more divisors than any number less than double itself (sequenceA072938 in theOEIS). Not only it is the 7th (and last) number with more divisors than any number double itself but is also the 7th number that is highly composite and the lowest common multiple of a consecutive set of integers from 1 (sequenceA095921 in theOEIS) which is a property the previous number with this pattern of divisors does not have (360). That is, although 360 and 2520 both have more divisors than any number twice themselves, 2520 is the lowest number divisible by both 1 to 9 and 1 to 10, whereas 360 is not the lowest number divisible by 1 to 6 (which60 is) and is not divisible by 1 to 7 (which420 is). It is also the 6th and largest highly composite number that is a divisor of every higher highly composite number (sequenceA106037 in theOEIS).
2521 –star prime, centered square number^[68]
2522 – Mertens function zero
2523 – Mertens function zero
2524 – Mertens function zero
2525 – Mertens function zero
2530 – Mertens function zero, Leyland number^[72]
2533 – Mertens function zero
2537 – Mertens function zero
2538 – Mertens function zero
2543 –Sophie Germain prime, sexy prime with 2549
2548 = 14³ - 14²
2549 –Sophie Germain prime,super-prime, sexy prime with 2543
2550 – pronic number^[54]
2552 – sum of the totient function for the first 91 integers
2556 – triangular number
2567 – Mertens function zero
2568 – Mertens function zero, number of digits in thedecimal expansion of 1000!, or theproduct of allnatural numbers from 1 to 1000
2570 – Mertens function zero
2579 –safe prime^[22]
2580 –Keith number,^[82] forms a column on a telephone orPIN pad
2584 –Fibonacci number,^[97] sum of the first 37 primes
2592 –3-smooth number (2⁵×3⁴)
2596 – sum of the totient function for the first 92 integers

2600 to 2699

[edit]

2600 – tetrahedral number,^[18] member of aRuth–Aaron pair with 2601 (first definition)
- 2600Hz is the tone used by ablue box to defeat toll charges onlong distance telephone calls
- 2600: The Hacker Quarterly is a magazine named after the above
- TheAtari 2600 was a popularvideo game console
2601 = 51², member of aRuth–Aaron pair with 2600 (first definition)
2609 –super-prime
2620 –telephone number,amicable number with 2924
2625 = acentered octahedral number^[42]
2626 – decagonal number^[41]
2628 – triangular number
2632 – number of consecutive baseball games played byCal Ripken Jr.
2633 – sum of twenty-five consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167)
2641 – centered pentagonal number^[24]
2647 –super-prime, centered heptagonal number^[65]
2652 – pronic number^[54]
2656 – sum of the totient function for the first 93 integers
2665 – centered square number^[68]
2674 – nonagonal number^[70]
2677 – balanced prime^[86]
2680 – number of11-queens problem solutions
2683 –super-prime
2689 – Mertens function zero, Proth prime^[67]
2693 –Sophie Germain prime
2699 –Sophie Germain prime

2700 to 2799

[edit]

2701 – triangular number,super-Poulet number^[39]
2702 – sum of the totient function for the first 94 integers
2704 = 52²
2707 –strong prime, model number for the concept supersonic airlinerBoeing 2707
2719 –super-prime, largest known odd number which cannot be expressed in the formx² +y² + 10z² wherex,y andz are integers.^[98] In 1997 it was conjectured that this is also the largest such odd number.^[99] It is now^[when?] known this is true if thegeneralized Riemann hypothesis is true.^[100]
2728 –Kaprekar number^[83]
2729 – highly cototient number^[64]
2731 – the onlyWagstaff prime with four digits,^[101]Jacobsthal prime
2736 – octahedral number^[84]
2741 –Sophie Germain prime, 400th prime number
2744 = 14³, palindromic in base 13 (1331₁₃)
2747 – sum of the first 38 primes
2749 –super-prime,cousin prime with 2753
2753 –Sophie Germain prime, Proth prime^[67]
2756 – pronic number^[54]
2774 – sum of the totient function for the first 95 integers
2775 – triangular number
2780 – member of the Mian–Chowla sequence^[23]
2783 – member of a Ruth–Aaron pair with 2784 (first definition)
2784 – member of a Ruth–Aaron pair with 2783 (first definition)
2791 – cuban prime^[85]

2800 to 2899

[edit]

2801 – first base 7repunit prime
2803 –super-prime
2806 –centered pentagonal number,^[24] sum of the totient function for the first 96 integers
2809 = 53², centered octagonal number^[19]
2813 – centered square number^[68]
2816 – number of parts in all compositions of 10^[102]
2819 –Sophie Germain prime,safe prime, sum of seven consecutive primes (383 + 389 + 397 + 401 + 409 + 419 + 421)^[22]
2821 – Carmichael number^[93]
2835 – odd abundant number,^[80] decagonal number^[41]
2843 – centered heptagonal prime^[103]
2850 – triangular number
2862 – pronic number^[54]
2870 – square pyramidal number^[66]
2871 – nonagonal number^[70]
2872 –tetranacci number^[104]
2875 – number of lines on aquintic threefold^[105]
2879 –safe prime^[22]
2897 –super-prime,Markov prime^[106]

2900 to 2999

[edit]

2902 – sum of thetotient function for the first 97 integers
2903 –Sophie Germain prime,safe prime,^[22] balanced prime^[86]
2909 –super-prime
2914 – sum of the first 39 primes
2915 – Lucas–Carmichael number^[12]
2916 = 54²
2924 – amicable number with 2620
2925 –magic constant ofn ×n normalmagic square andn-queens problem forn = 18, tetrahedral number,^[18] member of the Mian-Chowla sequence^[23]
2926 – triangular number
2939 –Sophie Germain prime
2944 – sum of the totient function for the first 98 integers
2963 –Sophie Germain prime,safe prime, balanced prime^[86]
2964 – number of parallelogram polyominoes with 11 cells^[107]
2965 – greater of second pair ofSmith brothers, centered square number^[68]
2969 –Sophie Germain prime
2970 –harmonic divisor number,^[108] pronic number^[54]
2976 – centered pentagonal number^[24]
2988 – number of reduced trees with 20 nodes^[109]
2989 – inhexadecimal, reads as "BAD"
2997 – 1000-gonal number^[110]
2999 –safe prime

Prime numbers

[edit]

There are 127prime numbers between 2000 and 3000:^[111]^[112]

2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999

References

[edit]

^Sloane, N. J. A. (ed.)."Sequence A052486 (Achilles numbers - powerful but imperfect: if n = Product(p_i^e_i) then all e_i > 1 (i.e., powerful), but the highest common factor of the e_i is 1, i.e., not a perfect power)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A006933 ('Eban' numbers (the letter 'e' is banned!))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A008537 (Numbers that do not contain the letter 'n'))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A007304 (Sphenic numbers: products of 3 distinct primes))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A022264 (n×(7×n - 1)/2)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A085945 (Number of subsets of {1,2,...,n} with relatively prime elements)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A064539 (Numbers n such that 2^n + n^2 is prime)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A001496 (Number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000740 (Number of 2n-bead balanced binary necklaces of fundamental period 2n, equivalent to reversed complement)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A056721 (Numbers n such that 8×10^n-1 is prime)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A001770 (Numbers k such that 5×2^k - 1 is prime)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^bSloane, N. J. A. (ed.)."Sequence A006972 (Lucas-Carmichael numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A194472 (Erdős-Nicolas numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^"Can you solve it? 2019 in numbers".the Guardian. 2018-12-31. Retrieved2021-09-19.
^Sloane, N. J. A. (ed.)."Sequence A294685 (non-isomorphic colorings of a toroidal n × k grid using exactly three colors under translational symmetry)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A141769 (Beginning of a run of 4 consecutive Niven (or Harshad) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A063416 (Multiples of 7 whose sum of digits is equal to 7)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^dSloane, N. J. A. (ed.)."Sequence A000292 (Tetrahedral numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^dSloane, N. J. A. (ed.)."Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A038547 (Least number with exactly n odd divisors.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A144959 (A134955(n) - A134955(n-1). Number of hyperforests spanning n unlabeled nodes without isolated vertices.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^kSloane, N. J. A. (ed.)."Sequence A005385 (Safe primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^e ^fSloane, N. J. A. (ed.)."Sequence A005282 (Mian-Chowla sequence)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^e ^f ^gSloane, N. J. A. (ed.)."Sequence A005891 (Centered pentagonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A051841 (Number of binary Lyndon words with an even number of 1's)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000107 (Number of rooted trees with n nodes and a single labeled node; pointed rooted trees; vertebrates)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A137917 (number of unlabeled graphs on n nodes whose components are unicyclic graphs)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A007408 (Wolstenholme numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000295 (Eulerian numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000325 (2^n - n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A002854 (Number of unlabeled Euler graphs with n nodes; number of unlabeled two-graphs with n nodes; number of unlabeled switching classes of graphs with n nodes; number of switching classes of unlabeled signed complete graphs on n nodes; number of Seidel matrices of order n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A027480 (n*(n+1)*(n+2)/2)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A005703 (Number of n-node connected graphs with at most one cycle)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A385344 (Numbers where all the digits of all the prime factors are smaller than 3)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A067538 (Number of partitions of n in which the number of parts divides n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A001158 (sigma_3(n): sum of cubes of divisors of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000918 (2^n - 2)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^bSloane, N. J. A. (ed.)."Sequence A050217 (Super-Poulet numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A003261 (Woodall numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^eSloane, N. J. A. (ed.)."Sequence A001107 (10-gonal (or decagonal) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^bSloane, N. J. A. (ed.)."Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A018900 (Sums of two distinct powers of 2)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A003350 (Numbers that are the sum of 5 positive 5th powers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A002618 (n*phi(n))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A001047 (3^n - 2^n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A066571 (Number of sets of positive integers with arithmetic mean n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A097646 (Numbers n such that n equals phi(phi(n) + sigma(n)))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A054735 (Sums of twin prime pairs)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A090022 (Number of distinct lines through the origin in the n-dimensional lattice of side length 6)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A011971 (Aitken's array)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A325858 (Number of Golomb partitions of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000013 (Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^jSloane, N. J. A. (ed.)."Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A006384 (Number of sensed planar maps with n edges)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A014206 (n^2 + n + 2)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A001469 (Genocchi numbers (of first kind); unsigned coefficients give expansion of x*tan(x/2))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A001181 (Number of Baxter permutations of length n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A053742 (Sum of odd numbers in range 10*n to 10*n+9)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A068932 (Number of disconnected regular graphs with n nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A307454 (a(n) is the number of canonical polygons with 2n edges having 2-fold rotational symmetry)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A056309 (Number of reversible strings with n beads using exactly two different colors)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A005585 (5-dimensional pyramidal numbers: n*(n+1)*(n+2)*(n+3)*(2n+3)/5!)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^cSloane, N. J. A. (ed.)."Sequence A100827 (Highly cototient numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^dSloane, N. J. A. (ed.)."Sequence A069099 (Centered heptagonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^b ^cSloane, N. J. A. (ed.)."Sequence A000330 (Square pyramidal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^b ^cSloane, N. J. A. (ed.)."Sequence A080076 (Proth primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^b ^c ^d ^e ^f ^gSloane, N. J. A. (ed.)."Sequence A001844 (Centered square numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A000957 (Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^eSloane, N. J. A. (ed.)."Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A067128 (Ramanujan's largely composite numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^bSloane, N. J. A. (ed.)."Sequence A076980 (Leyland numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A002411 (Pentagonal pyramidal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A008918 (Numbers n such that 4*n = (n written backwards))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-14.
^Sloane, N. J. A. (ed.)."Sequence A001190 (Wedderburn-Etherington numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Mackenzie, Dana (2018)."2184: An Absurd (and Adsurd) Tale".Integers.18.
^Sloane, N. J. A. (ed.)."Sequence A014575 (Vampire numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^bSloane, N. J. A. (ed.)."Sequence A082897 (Perfect totient numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A001006 (Motzkin numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^bSloane, N. J. A. (ed.)."Sequence A005231 (Odd abundant numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A005479 (Prime Lucas numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^bSloane, N. J. A. (ed.)."Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^bSloane, N. J. A. (ed.)."Sequence A006886 (Kaprekar numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^bSloane, N. J. A. (ed.)."Sequence A005900 (Octahedral numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^b ^cSloane, N. J. A. (ed.)."Sequence A002407 (Cuban primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^b ^c ^d ^eSloane, N. J. A. (ed.)."Sequence A006562 (Balanced primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A002110 (Primorial numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^"The Small Groups library". Archived fromthe original on 2007-02-04. Retrieved2008-01-22..
^Sloane, N. J. A. (ed.)."Sequence A005898 (Centered cube numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A069151 (Concatenations of consecutive primes, starting with 2, that are also prime)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A002104 (Logarithmic numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000129 (Pell numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^^a ^bSloane, N. J. A. (ed.)."Sequence A002997 (Carmichael numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000219 (Number of planar partitions (or plane partitions) of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000931 (Padovan sequence)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A000045 (Fibonacci numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^"Odd numbers that are not of the form x^2+y^2+10*z^2.".The Online Encyclopedia of Integer Sequences. The OEIS Foundation, Inc. Retrieved13 November 2012.
^Ono, Ken (1997)."Ramanujan, taxicabs, birthdates, zipcodes and twists"(PDF).American Mathematical Monthly.104 (10):912–917.CiteSeerX 10.1.1.514.8070.doi:10.2307/2974471.JSTOR 2974471. Archived fromthe original(PDF) on 15 October 2015. Retrieved11 November 2012.
^Ono, Ken; K Soundararajan (1997)."Ramanujan's ternary quadratic forms"(PDF).Inventiones Mathematicae.130 (3):415–454.Bibcode:1997InMat.130..415O.CiteSeerX 10.1.1.585.8840.doi:10.1007/s002220050191.S2CID 122314044. Archived fromthe original(PDF) on 18 July 2019. Retrieved12 November 2012.
^Sloane, N. J. A. (ed.)."Sequence A000979 (Wagstaff primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A001792 (a(n) = (n+2)*2^(n-1))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A144974 (Centered heptagonal prime numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A000078 (Tetranacci numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Pandharipande, Rahul (1998),"Rational curves on hypersurfaces (after A. Givental)",Astérisque, 1997/98 (252):307–340,arXiv:math/9806133,Bibcode:1998math......6133P,MR 1685628
^Sloane, N. J. A. (ed.)."Sequence A002559 (Markoff (or Markov) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A001599 (Harmonic or Ore numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A000014 (Number of series-reduced trees with n nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A195163 (1000-gonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-13.
^Sloane, N. J. A. (ed.)."Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Stein, William A. (10 February 2017)."The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture".wstein.org. Retrieved6 February 2021.

\mathbb {Z}

Integers

−2,−1

0 to 199

0 to 99	100 to 199
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99	100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199

200 to 399

200 to 299	300 to 399
200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299	300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399

400 to 999

400s, 500s, and 600s	700s, 800s, and 900s
400 420 440 495 496 500 501 511 512 555 600 610 613 616 666 693	700 720 743 744 777 786 800 801 836 840 880 881 888 900 911 971 987 999

1000s and 10,000s
1000s	1000 1001 1023 1024 1089 1093 1105 1234 1289 1458 1510 1728 1729 1980 1987 2000 2016 2520 3000 3511 4000 4104 5000 5040 6000 6174 7000 7744 7825 8000 8128 8192 9000 9855 9999
10,000s	10,000 16,807 20,000 30,000 40,000 50,000 60,000 64,079 65,535 65,536 65,537 70,000 80,000 90,000

100,000s to 10,000,000,000,000s
100,000 142,857 144,000 1,000,000 10,000,000 43,112,609 100,000,000 1,000,000,000 2,147,483,647 4,294,967,295 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000

Large numbers

Retrieved from "https://en.wikipedia.org/w/index.php?title=2000_(number)&oldid=1324023671#2400_to_2499"

Category:

Integers

Hidden categories:

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