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 A088315 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. 0
 5, 13, 7, 11, 53, 29, 21, 29, 89, 19, 89, 75, 89, 77, 189, 59, 61, 103, 185, 203, 189, 95, 167, 253, 107, 187, 79, 37, 289, 173, 257, 43, 169, 135, 175, 179, 155, 291, 189, 311, 155, 141, 157, 449, 119, 129, 349, 131, 609, 383, 391, 429, 409, 839, 201, 371, 425 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS FORMULA a(n) = nextprime(A088331(n)!+A088331(n)) - precprime(A088331(n)!) - 1. EXAMPLE There are 13 consecutive composite numbers between primes 113 < 5! and 127 > 5!+5. 13 is the second entry in the sequence. PROG (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", ")) ) } CROSSREFS Cf. A088331. Sequence in context: A089619 A094473 A068530 * A138296 A094474 A064109 Adjacent sequences:  A088312 A088313 A088314 * A088316 A088317 A088318 KEYWORD nonn AUTHOR Cino Hilliard, Nov 06 2003 EXTENSIONS Edited by Ray Chandler, Nov 10 2003 STATUS approved

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)