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

1,1

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.

Links

Table of n, a(n) for n=1..18.

Mathematica

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

Crossrefs

Cf. A090661, A089014.

Equals A002981 + 1.

Sequence in context: A000207 A002986 A147569 * A288140 A287594 A296271

Adjacent sequences: A090657 A090658 A090659 * A090661 A090662 A090663

Keyword

nonn

Author

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

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

Status

approved