cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-15 of 15 results.

A272042 a(n) = 2*prime(2n) - prime(n).

Original entry on oeis.org

4, 11, 21, 31, 47, 61, 69, 87, 99, 113, 127, 141, 161, 171, 179, 209, 219, 241, 259, 275, 289, 307, 315, 357, 361, 377, 399, 419, 433, 449, 459, 491, 497, 535, 549, 567, 589, 603, 627, 645, 663, 685, 695, 721, 729
Offset: 1

Views

Author

Andres Cicuttin, Apr 18 2016

Keywords

Examples

			For n=1, 2*prime(2*1)-prime(1) = 2*3 - 2 = 4.
For n=10, 2*prime(2*10)-prime(10) = 2*71 - 29 = 113.

Programs

  • Mathematica
    Table[2*Prime[2 n] - Prime[n], {n, 1, 45}]
  • PARI
    a(n) = 2*prime(2*n) - prime(n) \\ Charles R Greathouse IV, Apr 18 2016

Formula

a(n) = 3n*log n + 3n*log log n - (3-log 2)*n + O(n log log n/log n). - Charles R Greathouse IV, Apr 18 2016
a(n) = A072473(n) + A031215(n). - R. J. Mathar, Apr 20 2016

A066894 Numbers k such that prime(2*k) - prime(k) == 0 (mod k).

Original entry on oeis.org

1, 2, 4, 6, 18, 42, 44, 49, 246, 257, 259, 272, 283, 294, 25284, 62648, 62664, 62673, 62700, 62701, 158706, 404835, 404859, 405119, 405448, 405451, 2630908, 2630929, 2631249, 2631303, 2631368, 2631414, 2631509, 2631517, 2631576, 2631666, 17405852, 44932936
Offset: 1

Views

Author

Benoit Cloitre, Jan 24 2002

Keywords

Examples

			prime(2*2) - prime(2) = 7 - 3 = 4 that is equal to 0 mod 2, so 2 is in the sequence.

Crossrefs

Cf. A072473.

Programs

  • PARI
    isok(n) = (prime(2*n)-prime(n)) % n == 0; \\ Michel Marcus, Nov 20 2013

Extensions

a(15)-a(20) from Michel Marcus, Nov 20 2013
a(21)-a(38) from Donovan Johnson, Nov 20 2013

A141644 Primes of the form (p(2n)-p(n))/(7*2), where p(n)=n-th prime.

Original entry on oeis.org

3, 19, 41, 173, 181, 281, 347, 373, 401, 409, 433, 449, 461, 461, 479, 499, 509, 541, 547, 571, 577, 619, 691, 701, 709, 859, 881, 919, 929, 1087, 1091, 1093, 1097, 1193, 1229, 1367, 1367, 1481, 1483, 1511, 1523, 1553, 1559, 1579, 1601, 1667, 1697, 1699
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Sep 18 2008

Keywords

Examples

			If n=10, then (p(10*2)-p(10))/7*2=(71-29)/14=3=a(1).
If n=45, then (p(45*2)-p(45))/7*2=(463-197)/14=19=a(2).
If n=85, then (p(85*2)-p(85))/7*2=(1013-439)/14=41=a(3).
If n=300, then (p(300*2)-p(300))/7*2=(4409-1987)/14=173=a(4).
If n=311, then (p(311*2)-p(311))/7*2=(4597-2063)/14=181=a(5).
If n=459, then (p(459*2)-p(459))/7*2=(7187-3253)/14=281=a(6), etc.

Crossrefs

Cf. A000040.
Cf. A072473. [From R. J. Mathar, Oct 04 2008]

Programs

  • Mathematica
    Select[Table[(Prime[2n]-Prime[n])/14,{n,3000}],PrimeQ] (* Harvey P. Dale, Feb 01 2019 *)

Extensions

More terms from R. J. Mathar, Oct 04 2008
Definition clarified by Harvey P. Dale, Feb 01 2019

A214612 prime(n^3) - prime(n).

Original entry on oeis.org

0, 16, 98, 304, 680, 1308, 2292, 3652, 5496, 7890, 10926, 14716, 19362, 24766, 31272, 38820, 47598, 57498, 68964, 81728, 96064, 112212, 129990, 149628, 171432, 194942, 220758, 248744, 279322, 312470, 347580, 385962, 427032, 470794, 517404, 567720, 620374
Offset: 1

Views

Author

Jonathan Vos Post, Mar 06 2013

Keywords

Comments

This is to exponent 3 as A213926 is to exponent 2.

Examples

			a(1) = prime(1^3) - prime(1) = 2-2 = 0.
a(2) = prime(2^3) - prime(2) = 19-3 = 16.
a(3) = prime(3^3) - prime(3) = 103-5 = 98.

Crossrefs

Cf. A000040, A001223, A031131, A031165-A031172, A072473, A092504, A213926.

Programs

  • Mathematica
    Table[Prime[n^3] - Prime[n], {n, 50}] (* T. D. Noe, Mar 07 2013 *)

A275988 a(n) = prime(3n) - prime(n).

Original entry on oeis.org

3, 10, 18, 30, 36, 48, 56, 70, 80, 84, 106, 114, 126, 138, 150, 170, 174, 190, 202, 210, 234, 238, 264, 270, 282, 296, 316, 326, 340, 350, 360, 372, 386, 418, 422, 442, 450, 456, 476, 486, 498, 520, 536, 550, 564, 588, 600, 604, 626, 634, 650, 672, 696, 702, 720, 734, 750, 762, 774
Offset: 1

Views

Author

Terry D. Grant, Aug 15 2016

Keywords

Examples

			For n=3, prime(3n) = 23, and prime(n) = 5, therefore a(3) = 23 - 5 = 18.

Crossrefs

Cf. A000040, A031336, A072473.

Programs

  • Mathematica
    Table[Prime[3n] - Prime[n], {n, 1, 100}]
  • PARI
    a(n) = prime(3*n) - prime(n); \\ Michel Marcus, Aug 18 2016

Formula

a(n) = A031336(n) - A000040(n).
Previous Showing 11-15 of 15 results.

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