A088331 Numbers n such that all numbers between the largest prime preceding n! and the smallest prime following n! + n are composite.

4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 78, 79, 80

Offset

1,1

Links

Table of n, a(n) for n=1..71.

Example

For n = 7 there are 11 consecutive primes (5040-5050) between primes 5039 and 5051. 7 is the 4th entry in the sequence. 11 does not appear because 11!+1 is prime.

Mathematica

allCompQ[n_]:=Module[{nf=n!}, AllTrue[Range[NextPrime[nf, -1]+1, NextPrime[nf+n]-1], CompositeQ]]; Select[Range[80], allCompQ] (* Harvey P. Dale, Jul 15 2023 *)

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(n", ")) ) }

Crossrefs

Sequence in context: A214421 A294237 A162706 * A239433 A014091 A308040

Adjacent sequences: A088328 A088329 A088330 * A088332 A088333 A088334

Keyword

nonn

Author

Cino Hilliard, Nov 06 2003

Extensions

More terms from Ray Chandler, Nov 09 2003

Status

approved