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.

A167132 Gaps between twin prime pairs.

Original entry on oeis.org

0, 4, 4, 10, 10, 16, 10, 28, 4, 28, 10, 28, 10, 4, 28, 10, 28, 10, 28, 34, 70, 10, 28, 58, 46, 28, 16, 22, 16, 148, 10, 4, 28, 22, 136, 10, 16, 10, 28, 58, 76, 46, 10, 10, 16, 106, 22, 28, 4, 118, 10, 46, 28, 22, 64, 82, 4, 52, 16, 46, 28, 52, 4, 22, 16, 10, 94, 28, 40, 28, 40, 166
Offset: 1

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Author

Oleg Zyakun, Oct 28 2009

Keywords

Comments

Let G_n denote the twins gap between two consecutive twins, thus a twins gap is the difference between two consecutive twins (p_n, p_n+2) and (p_m, p_m+2), i.e., the difference between p_m and p_n+2. G_n = p_m - (p_n +2) We have: G_1 = 0, G_2 = 4, G_3 = 4, G_4 = 10.

Programs

  • Maple
    A001359 := proc(n) if n = 1 then 3; else a := nextprime(procname(n-1)) ; while not isprime(a+2) do a := nextprime(a) ; od: return a; fi; end: A006512 := proc(n) A001359(n)+2 ; end: A167132 := proc(n) A001359(n+1)-A006512(n) ; end: seq(A167132(n),n=1..120) ; # R. J. Mathar, Oct 29 2009
  • Mathematica
    ps = Prime[Range[1000]]; p2 = Flatten[Position[Differences[ps], 2]]; Differences[ps[[p2]]] - 2 (* T. D. Noe, Jan 10 2012 *)

Formula

a(n) = A001359(n+1) - A006512(n). - R. J. Mathar, Oct 29 2009