From Wikipedia, the free encyclopedia
Natural number
It is:
Selected numbers in the range 2001–2999
2001 to 2099
2001 –
sphenic number
[4]
2002 –
palindromic number in
decimal , 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 24th
crystagon
[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 X 4 matrices with nonnegative integer entries and row and column sums equal to 3
[8]
2009 = 74 − 73 − 72
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 the
totient function for the first 81 integers
2021 = 43 * 47, consecutive
prime 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 , sum of the cubes of the first nine positive integers (and therefore square of the sum of the first nine positive integers),
centered octagonal number ;
[19] least number with 15
odd divisors
[20]
2026 = Number of hyperforests spanning 10 unlabeled nodes without isolated vertices
[21]
2027 –
super-prime ,
safe prime
[22]
2028 = 133 – 132
2029 – member of the
Mian–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 – the fractional part of
(
3
2
)
2033
{\displaystyle \left({\frac {3}{2}}\right)^{2033}}
decreases monotonically to zero
[26]
2039 –
Sophie Germain prime ,
safe prime
[22]
2045 – number of
partially ordered set with 7 unlabeled elements
[27]
2047 –
super-Poulet number ,
[28]
Woodall number ,
[29]
decagonal number ,
[30] a
centered octahedral number ,
[31] 2047 = 211 - 1 = 23 × 89 and is the first
Mersenne number that is composite for a prime exponent
2048 =
211
2050 – sum of 2 consecutive odd squares (31² + 33²)
2053 –
star number
2056 –
magic constant of n × n normal
magic square and
n -queens problem for n = 16
2060 – sum of the
totient function for the first 82 integers
2063 –
Sophie Germain prime ,
safe prime ,
[22]
super-prime
2068 – number of 16-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
[32]
2069 –
Sophie Germain prime
2070 –
pronic number
[33]
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
[34]
2100 to 2199
2100 – Mertens function zero
2101 –
centered heptagonal number
[35]
2107 – member of a
Ruth–Aaron pair with 2108 (first definition)
2108 – member of a Ruth–Aaron pair with 2107 (first definition)
2109 –
square pyramidal number ,
[36] the sum of the third and last trio of three-digit
permutable primes in
decimal :
199 +
919 +
991
2112 – The break-through
album of the band
Rush
2113 – Mertens function zero,
Proth prime ,
[37]
centered square number
[38]
2116 = 462
2117 – Mertens function zero
2119 – Mertens function zero
2120 – Mertens function zero, Fine number
[39]
2122 – Mertens function zero
2125 –
nonagonal number
[40]
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 22π 4
2145 – triangular number
2153 – with 2161, smallest consecutive primes that have the same sum of digits as each other's prime indices
2161 – with 2153, smallest consecutive primes that have the same sum of digits as each other's prime indices
2162 – pronic number
[33]
2166 – sum of the totient function for the first 84 integers
2169 –
Leyland number
[41]
2171 – Mertens function zero
2172 – Mertens function zero
2175 – smallest number requiring 143 seventh powers for Waring representation
2176 –
pentagonal pyramidal number ,
[42] centered pentagonal number
[24]
2178 – first natural number whose digits in its decimal representation get reversed when multiplied by 4
[43]
2179 –
Wedderburn–Etherington prime
[44]
2184 – equals both 37 − 3 and 133 − 13 and is believed to be the only such doubly strictly absurd number
[45] [
unreliable source? ]
2187 =
37 ,
vampire number ,
[46]
perfect totient number
[47]
2188 –
Motzkin number
[48]
2197 = 133 , palindromic in base 12 (133112 )
2199 – perfect totient number
[47]
2200 to 2299
2300 to 2399
2300 – tetrahedral number,
[18] member of a Ruth–Aaron pair with 2299 (first definition)
2301 – nonagonal number
[40]
2304 = 482
2306 – Mertens function zero
2309 –
primorial prime ,
twin prime with 2311, Mertens function zero, highly cototient number
[34]
2310 – fifth
primorial
[56]
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
[57]
2331 –
centered cube number
[58]
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
[33]
2357 –
Smarandache–Wellin prime
[59]
2368 – sum of the totient function for the first 88 integers
2372 – logarithmic number
[60]
2378 –
Pell number
[61]
2379 – member of the Mian–Chowla sequence
[23]
2381 –
super-prime , centered square number
[38]
2383 (2384) – number of delegates required to win the
2016 Democratic Party presidential primaries (out of 4051)
2393 –
Sophie Germain prime
2397 – sum of the squares of the first ten primes
2399 –
Sophie Germain prime
2400 to 2499
2400 – perfect score on
SAT tests administered after 2005
2401 = 492 = 74 , centered octagonal number
[19]
2415 – triangular number
2417 –
super-prime , balanced prime
[55]
2425 – decagonal number
[30]
2427 – sum of the first 36 primes
2431 – product of three consecutive primes
2437 – cuban prime,
[54] largest
right-truncatable prime in base 5
2447 –
safe prime
[22]
2450 – pronic number
[33]
2456 – sum of the totient function for the first 89 integers
2458 – centered heptagonal number
[35]
2459 –
Sophie Germain prime ,
safe prime
[22]
2465 –
magic constant of n × n normal
magic square and
n -queens problem for n = 17,
Carmichael number
[62]
2470 – square pyramidal number
[36]
2471 – number of ways to partition {1,2,3,4,5,6} and then partition each cell (block) into subcells
[63]
2477 –
super-prime ,
cousin prime
2480 – sum of the totient function for the first 90 integers
2481 – centered pentagonal number
[24]
2484 – nonagonal number
[40]
2485 – triangular number, number of planar partitions of 13
[64]
2491 = 47 * 53, consecutive
prime numbers , member of
Ruth–Aaron pair with 2492 under second definition
2492 – member of Ruth–Aaron pair with 2491 under second definition
2500 to 2599
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 the
Padovan sequence
[65]
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 numbers
1 , 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 (sequence
A072938 in the
OEIS ). 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 (sequence
A095921 in the
OEIS ) 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 (which
60 is) and is not divisible by 1 to 7 (which
420 is). It is also the 6th and largest highly composite number that is a divisor of every higher highly composite number (sequence
A106037 in the
OEIS ).
2521 –
star prime , centered square number
[38]
2522 – Mertens function zero
2523 – Mertens function zero
2524 – Mertens function zero
2525 – Mertens function zero
2530 – Mertens function zero, Leyland number
[41]
2533 – Mertens function zero
2537 – Mertens function zero
2538 – Mertens function zero
2543 –
Sophie Germain prime , sexy prime with 2549
2549 –
Sophie Germain prime ,
super-prime , sexy prime with 2543
2550 – pronic number
[33]
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 the
decimal expansion of 1000
! , or the
product of all
natural numbers from 1 to 1000
2570 – Mertens function zero
2579 –
safe prime
[22]
2580 –
Keith number ,
[51] forms a column on a telephone or
PIN pad
2584 –
Fibonacci number ,
[66] 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
2700 to 2799
2800 to 2899
2900 to 2999
Prime numbers
There are 127
prime numbers between 2000 and 3000:
[80]
[81]
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
^
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)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A006933 ('Eban' numbers (the letter 'e' is banned!))" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A008537 (Numbers that do not contain the letter 'n'))" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A007304 (Sphenic numbers: products of 3 distinct primes))" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A022264 (n*(7*n - 1)/2)" . The
On-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)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A064539 (Numbers n such that 2^n + n^2 is prime)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A001496 (Number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to n)" . The
On-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)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A056721 (Numbers n such that 8*10^n-1 is prime)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A006972 (Lucas-Carmichael numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A194472 (Erdős-Nicolas numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
"Can you solve it? 2019 in numbers" . the Guardian . 2018-12-31. Retrieved 2021-09-19 .
^
Sloane, N. J. A. (ed.).
"Sequence A294685 (non-isomorphic colorings of a toroidal n X k grid using exactly three colors under translational symmetry)" . The
On-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)" . The
On-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)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
d
Sloane, N. J. A. (ed.).
"Sequence A000292 (Tetrahedral numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
d
Sloane, N. J. A. (ed.).
"Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A038547 (Least number with exactly n odd divisors.)" . The
On-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.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
d
e
f
g
h
i
j
k
Sloane, N. J. A. (ed.).
"Sequence A005385 (Safe primes)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
d
e
f
Sloane, N. J. A. (ed.).
"Sequence A005282 (Mian-Chowla sequence)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
d
e
f
g
Sloane, N. J. A. (ed.).
"Sequence A005891 (Centered pentagonal numbers)" . The
On-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)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A081464 (Numbers k such that the fractional part of (3/2)^k decreases monotonically to zero)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A050217 (Super-Poulet numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A003261 (Woodall numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
d
e
Sloane, N. J. A. (ed.).
"Sequence A001107 (10-gonal (or decagonal) numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))" . The
On-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)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
d
e
f
g
h
i
j
Sloane, N. J. A. (ed.).
"Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
Sloane, N. J. A. (ed.).
"Sequence A100827 (Highly cototient numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
d
Sloane, N. J. A. (ed.).
"Sequence A069099 (Centered heptagonal numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
c
Sloane, N. J. A. (ed.).
"Sequence A000330 (Square pyramidal numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
c
Sloane, N. J. A. (ed.).
"Sequence A080076 (Proth primes)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
c
d
e
f
g
Sloane, N. J. A. (ed.).
"Sequence A001844 (Centered square numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
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)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
a
b
c
d
e
Sloane, N. J. A. (ed.).
"Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A076980 (Leyland numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A002411 (Pentagonal pyramidal numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A008918 (Numbers n such that 4*n = (n written backwards))" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-14 .
^
Sloane, N. J. A. (ed.).
"Sequence A001190 (Wedderburn-Etherington numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^ Mackenzie, Dana (2018).
"2184: An Absurd (and Adsurd) Tale" . Integers . 18 .
^
Sloane, N. J. A. (ed.).
"Sequence A014575 (Vampire numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A082897 (Perfect totient numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A001006 (Motzkin numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A005231 (Odd abundant numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A005479 (Prime Lucas numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A006886 (Kaprekar numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A005900 (Octahedral numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
c
Sloane, N. J. A. (ed.).
"Sequence A002407 (Cuban primes)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
c
d
e
Sloane, N. J. A. (ed.).
"Sequence A006562 (Balanced primes)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A002110 (Primorial numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
"The Small Groups library" . Archived from
the original on 2007-02-04. Retrieved 2008-01-22 . .
^
Sloane, N. J. A. (ed.).
"Sequence A005898 (Centered cube numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A069151 (Concatenations of consecutive primes, starting with 2, that are also prime)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A002104 (Logarithmic numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A000129 (Pell numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
a
b
Sloane, N. J. A. (ed.).
"Sequence A002997 (Carmichael numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A000219 (Number of planar partitions (or plane partitions) of n)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A000931 (Padovan sequence)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A000045 (Fibonacci numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
"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. Retrieved 13 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 from
the original (PDF) on 15 October 2015. Retrieved 11 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 from
the original (PDF) on 18 July 2019. Retrieved 12 November 2012 .
^
Sloane, N. J. A. (ed.).
"Sequence A000979 (Wagstaff primes)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A001792 (a(n) = (n+2)*2^(n-1))" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A144974 (Centered heptagonal prime numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A000078 (Tetranacci numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^ 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)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A001599 (Harmonic or Ore numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A000014 (Number of series-reduced trees with n nodes)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A195163 (1000-gonal numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-06-13 .
^
Sloane, N. J. A. (ed.).
"Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)" . The
On-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 . Retrieved 6 February 2021 .
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