

A167132


Gaps between twin prime pairs.


3



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
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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(n1)) ; 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



