A167132 Gaps between twin prime pairs.

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

1,2

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.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Program to generate the sequence

Formula

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

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 *)

Crossrefs

Sequence in context: A220044 A219828 A219714 * A168326 A101256 A116569

Adjacent sequences: A167129 A167130 A167131 * A167133 A167134 A167135

Keyword

nonn

Author

Oleg Zyakun, Oct 28 2009

Status

approved