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%I #8 Oct 19 2017 10:38:27
%S 3,4,12,28,38,42,74,78,117,155,321,341,400,428,873,1478,6381,26952
%N Numbers n such that n*nextprime((n-1)!)-nextprime(n!) < 0.
%C 3*nextprime((3-1)!) - nextprime(3!) = 3*nextprime(2!) - nextprime(3!) = 3*2 - 7 = -1.
%C For n>2 n!+1 is prime <==> nextprime((n+1)!)>(n+1)nextprime(n!) and we can conjecture that for n>2 if n!+1 is prime then (n+1)!+1 is not prime.
%t NextPrim[ n_ ] := Block[ {k = n + 1}, While[ !PrimeQ[ k ], k++ ]; k ]; Select[ Range[ 260 ], #*NextPrim[ (# - 1)! ] - NextPrim[ #! ] < 0 & ] (* _Robert G. Wilson v_ *)
%Y Cf. A090661, A089014.
%Y Equals A002981 + 1.
%K nonn
%O 1,1
%A Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Dec 15 2003
%E Better description from _Don Reble_, Dec 20 2003
%E Three more terms from _Robert G. Wilson v_, Dec 20 2003
%E a(14) from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Jan 05 2004