

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 ksemiprime for some k >= 2.


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
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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 ksemiprime.


EXAMPLE

a(27)=10 since prime(69)prime(68)=347337=10.


MAPLE

L:=[]: cnt:=0; for z to 1 do for k from 1 to 200 do p:=ithprime(k); q:=nextprime(p); x:=qp; 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: A021019 A177057 A082510 * A082509 A226280 A103337
Adjacent sequences: A113424 A113425 A113426 * A113428 A113429 A113430


KEYWORD

nonn


AUTHOR

Walter Kehowski, Jan 08 2006


STATUS

approved



