A113427 If d(n) is the sequence of prime differences, d(n) = prime(n+1) - prime(n), then a(n) is the subsequence of d(n) such that d(n) is nonprime and squarefree. Except for the initial term of 1, the terms are k-semiprime for some k >= 2.

1, 6, 6, 6, 6, 6, 6, 6, 14, 6, 10, 6, 6, 6, 6, 10, 6, 10, 6, 6, 6, 6, 10, 14, 14, 6, 10, 6, 6, 6, 6, 10, 10, 6, 6, 6, 6, 10, 6, 6, 6, 10, 6, 6, 6, 6, 10, 6, 6, 6, 10, 10, 6, 6, 6, 14, 10, 10, 10, 14, 14, 10, 6, 6, 14, 6, 6, 6, 6, 10, 6, 10, 10, 6, 6, 6, 6, 6, 22, 10, 10, 6, 6, 6, 6

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..2000

Formula

a(k) = p(n+1) - p(n), if n=1, or p(n+1) - p(n) is k-semiprime.

Example

a(27)=10 since prime(69)-prime(68)=347-337=10.

Maple

L:=[]: cnt:=0; for z to 1 do for k from 1 to 200 do p:=ithprime(k); q:=nextprime(p); x:=q-p; if not(isprime(x)) and numtheory[issqrfree](x) then cnt:=cnt+1; L:=[op(L), [cnt, k, x]] fi od od; L;

Mathematica

Select[Differences[Prime[Range[300]]], !PrimeQ[#]&&SquareFreeQ[#]&] (* Harvey P. Dale, May 07 2015 *)

Crossrefs

Cf. A000040, A000469, A001358.

Sequence in context: A082510 A343195 A173068 * A082509 A226280 A331944

Adjacent sequences: A113424 A113425 A113426 * A113428 A113429 A113430

Keyword

nonn

Author

Walter Kehowski, Jan 08 2006

Status

approved