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%I #5 Oct 01 2013 17:57:44
%S 5,13,7,11,53,29,21,29,89,19,89,75,89,77,189,59,61,103,185,203,189,95,
%T 167,253,107,187,79,37,289,173,257,43,169,135,175,179,155,291,189,311,
%U 155,141,157,449,119,129,349,131,609,383,391,429,409,839,201,371,425
%N For n such that all numbers between the largest prime preceding n! and the smallest prime following n! + n are composite (see A088331), sequence is number of such consecutive composite numbers.
%F a(n) = nextprime(A088331(n)!+A088331(n)) - precprime(A088331(n)!) - 1.
%e There are 13 consecutive composite numbers between primes 113 < 5! and 127 > 5!+5. 13 is the second entry in the sequence.
%o (PARI) factgaps2(m) = { for(n=2,m, c=0; f=0; nf=n!; for(x=precprime(nf),nextprime(nf+n), if(isprime(nf+1),f=1; break); if(!isprime(x),c++) ); if(f==0,print1(c",")) ) }
%Y Cf. A088331.
%K nonn
%O 2,1
%A _Cino Hilliard_, Nov 06 2003
%E Edited by _Ray Chandler_, Nov 10 2003
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