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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 (list; graph; refs; listen; history; text; internal format)
 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: A021019 A177057 A082510 * A082509 A226280 A103337 Adjacent sequences:  A113424 A113425 A113426 * A113428 A113429 A113430 KEYWORD nonn AUTHOR Walter Kehowski, Jan 08 2006 STATUS approved

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Last modified January 22 08:20 EST 2019. Contains 319357 sequences. (Running on oeis4.)