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.

Showing 1-4 of 4 results.

A072473 a(n) = prime(2*n) - prime(n).

Original entry on oeis.org

1, 4, 8, 12, 18, 24, 26, 34, 38, 42, 48, 52, 60, 64, 66, 78, 80, 90, 96, 102, 108, 114, 116, 134, 132, 138, 148, 156, 162, 168, 166, 180, 180, 198, 200, 208, 216, 220, 230, 236, 242, 252, 252, 264, 266, 280, 280, 280, 294, 312, 324, 330, 336, 342, 344, 350, 350
Offset: 1

Views

Author

Amarnath Murthy, Jun 20 2002

Keywords

Comments

a(n) > prime(n) for n > 1. - Charles R Greathouse IV, Nov 22 2013
Sequence is not monotonic. - Zak Seidov, Feb 15 2015

Links

Crossrefs

Cf. A072715.

Programs

  • Magma
    [NthPrime(2*n) - NthPrime(n): n in [1..80]]; // Vincenzo Librandi, Feb 16 2015
  • Mathematica
    Table[ Prime[2n] - Prime[n], {n, 1, 60}]
  • PARI
    a(n) = prime(2*n) - prime(n); \\ Michel Marcus, Nov 22 2013

Formula

a(n) = A066066(n) + A000040(n). - Reinhard Zumkeller, Jul 25 2010

Extensions

Edited by Robert G. Wilson v and Jim Nastos, Jun 21 2002

A255171 First differences of A072473.

Original entry on oeis.org

3, 4, 4, 6, 6, 2, 8, 4, 4, 6, 4, 8, 4, 2, 12, 2, 10, 6, 6, 6, 6, 2, 18, -2, 6, 10, 8, 6, 6, -2, 14, 0, 18, 2, 8, 8, 4, 10, 6, 6, 10, 0, 12, 2, 14, 0, 0, 14, 18, 12, 6, 6, 6, 2, 6, 0, 20, 0, 8
Offset: 1

Views

Author

Zak Seidov, Feb 15 2015

Keywords

Links

Crossrefs

Cf. A072473, A072715.

Formula

a(n) = A072473(n+1) - A072473(n).

A258934 Half the difference between the 2n-th prime and the n-th prime, starting from n=2.

Original entry on oeis.org

2, 4, 6, 9, 12, 13, 17, 19, 21, 24, 26, 30, 32, 33, 39, 40, 45, 48, 51, 54, 57, 58, 67, 66, 69, 74, 78, 81, 84, 83, 90, 90, 99, 100, 104, 108, 110, 115, 118, 121, 126, 126, 132, 133, 140, 140, 140, 147, 156, 162, 165, 168, 171, 172, 175, 175, 185, 185, 189
Offset: 2

Views

Author

Federico Provvedi, Jun 15 2015

Keywords

Comments

The differences between odd prime numbers are always even, so a(n) is well defined for n>=2.

Links

Crossrefs

Cf. A072473, A072715, A087461.

Programs

  • Magma
    [(NthPrime(2*n)-NthPrime(n))/2: n in [2..60]]; // Bruno Berselli, Jun 15 2015
  • Mathematica
    Table[(Prime[2 k] - Prime[k])/2, {k, 2, 60}]
  • Sage
    [(nth_prime(2*n)-nth_prime(n))/2 for n in (2..60)] # Bruno Berselli, Jun 15 2015

Formula

a(n) = ( prime(2*n) - prime(n) ) / 2.
a(n) = A072473(n)/2.

A255172 Integers k such that A072473(k) = A072473(k+1) = A072473(k+2) = A072473(k+3).

Original entry on oeis.org

126, 15190, 15924, 17180, 23047, 24410, 33553, 44049, 51019, 54358, 74240, 77460, 102494, 103168, 128522, 154518, 156386, 186056, 232346, 244086, 250216, 285095, 291306, 320942, 447634, 465803, 477517, 478415, 508078, 518164, 518861, 526764, 587712, 589208
Offset: 1

Views

Author

Zak Seidov, Feb 15 2015

Keywords

Comments

Corresponding values of A072473(k): 900, 188790, 199218, 216630, 297504, 316572, 446890, 599998, 702990, 752700, 1052898, 1101480, 1488444, 1498860.

Links

Crossrefs

Cf. A072473, A072715, A255171.

Programs

  • PARI
    { my(p=0, q=0, k=0, r=0); for(n=1, 1e6, p=nextprime(1+p); q=nextprime(1+nextprime(1+q)); my(t=q-p); if(t<>r, r=t; k=0); k++; if(k>=4, print1(n+1-k, ", "))) } \\ Andrew Howroyd, Nov 11 2018

Extensions

Terms a(19) and beyond from Andrew Howroyd, Nov 11 2018
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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