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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.
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
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
KEYWORD
nonn
AUTHOR
Walter Kehowski, Jan 08 2006
STATUS
approved