A090704 Numbers k such that k*k! - 1 is prime.

2, 3, 5, 7, 8, 11, 27, 77, 98, 183, 285, 290, 397, 410, 599, 717, 731, 888, 1962, 2239, 2241, 2532, 8799, 11402, 18334, 20276, 21028

Offset: 1

Author

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Jan 15 2004

Keywords

• nonn
• more

Examples

			5 is a term since 5*5! - 1 = 599 is prime.
		

Crossrefs

Cf. A049433.

Programs

Mathematica

Select[Range[2600],PrimeQ[#(#!)-1]&] (* Because a(22) generates a 7524 digit number to be tested for primality, the program takes a long time to run. *) (* Harvey P. Dale, May 27 2014 *)

Formula

a(n) = A049433(n) - 1 because n! - (n-1)! - 1 = (n-1)*(n-1)! - 1.

Extensions

More terms from Farideh Firoozbakht, Oct 31 2004

a(23)-a(24) using A049433 from Michel Marcus, May 29 2014

a(25)-a(27) from Michael S. Branicky, Jun 13 2025