A099350 Numbers k such that 4*k! - 1 is prime.

0, 1, 2, 3, 5, 6, 10, 11, 51, 63, 197, 313, 579, 1264, 2276, 2669, 4316, 4382, 4678, 7907, 10843

Offset: 1

Author

Brian Kell, Oct 12 2004

Keywords

• nonn
• hard
• more

Comments

a(19) > 4570. - Jinyuan Wang, Feb 04 2020

Examples

			k = 5 is here because 4*5! - 1 = 479 is prime.
		

Crossrefs

Cf. A076680.

Cf. A002982, A076133, A076134, A099351, A180627, A180628, A180629, A180630, A180631.

Programs

Maple

for n from 0 to 1000 do if isprime(4*n! - 1) then print(n) end if end do;

Mathematica

For[n = 0, True, n++, If[PrimeQ[4 n! - 1], Print[n]]] (* Jean-François Alcover, Sep 23 2015 *)

PARI

is_A099350(n)=ispseudoprime(n!*4-1) \\ M. F. Hasler, Sep 20 2015

Extensions

a(14) from Alois P. Heinz, Sep 21 2015

a(15)-a(16) from Jean-François Alcover, Sep 23 2015

a(17)-a(18) from Jinyuan Wang, Feb 04 2020

a(19) from Michael S. Branicky, May 16 2023

a(20)-a(21) from Michael S. Branicky, Jul 11 2024