A090660 Numbers n such that n*nextprime((n-1)!)-nextprime(n!) < 0.

3, 4, 12, 28, 38, 42, 74, 78, 117, 155, 321, 341, 400, 428, 873, 1478, 6381, 26952

Offset: 1

Author

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Dec 15 2003

Keywords

• nonn

Comments

3*nextprime((3-1)!) - nextprime(3!) = 3*nextprime(2!) - nextprime(3!) = 3*2 - 7 = -1.

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.

Crossrefs

Cf. A090661, A089014.

Equals A002981 + 1.

Programs

Mathematica

NextPrim[ n_ ] := Block[ {k = n + 1}, While[ !PrimeQ[ k ], k++ ]; k ]; Select[ Range[ 260 ], #*NextPrim[ (# - 1)! ] - NextPrim[ #! ] < 0 & ] (* Robert G. Wilson v *)

Extensions

Better description from Don Reble, Dec 20 2003

Three more terms from Robert G. Wilson v, Dec 20 2003

a(14) from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Jan 05 2004