OFFSET
1,1
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
KEYWORD
nonn
AUTHOR
Cino Hilliard, Nov 06 2003
EXTENSIONS
More terms from Ray Chandler, Nov 09 2003
STATUS
approved