A096225 a(0) = 1; for n >= 0, a(n+1) = smallest prime factor of a(n)! + 1.

1, 2, 3, 7, 71, 6653, 25469, 15750503

Offset: 0

Author

N. J. A. Sloane, Aug 09 2004

Keywords

• nonn
• more
• hard
• nice

Examples

			71!+1 is the product of 6653 and a large prime.
		

Crossrefs

Cf. A002583, A051301.

Programs

Mathematica

a[1] = 2; a[n_] := Block[{p = PrimePi[a[n - 1]] + 1, r = a[n - 1]! + 1}, While[ Mod[r, Prime[p]] != 0, p++ ]; Prime[p]]; Do[ Print[ a[n]], {n, 7}] (* Robert G. Wilson v, Aug 12 2004 *)
NestList[FactorInteger[#!+1][[1,1]]&,1,7] (* Harvey P. Dale, Sep 20 2016 *)

Extensions

a(6) and a(7) from Robert G. Wilson v, Aug 12 2004