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.

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

Offset

2,1

Links

Table of n, a(n) for n=2..58.

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: A094473 A068530 A340802 * 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