A376644 Numbers k such that !k * k! + 1 = A003422(k) * A000142(k) + 1 = A061640(k) + 1 is prime.

1, 2, 4, 6, 13, 14, 21, 41, 64, 110, 268, 1196, 3083, 5201, 7496, 9698

Offset: 1

Author

Amiram Eldar, Oct 01 2024

Keywords

• nonn
• more

Comments

a(1)-a(11) were found by Earls (2003-2004).

The corresponding primes are 2, 5, 241, 110881, 3256459844769331201, ... .

Links

• Jason Earls, Marching Primes: !N x N! + 1, Journal of Recreational Mathematics, Vol. 32, No. 2 (2003-2004), pp. 123-124.

Crossrefs

Cf. A000142, A003422, A061640.

Programs

Mathematica

Select[Range[300], PrimeQ[#! * Sum[k!, {k, 0, #-1}] + 1] &]

PARI

is(k) = isprime(k! * sum(i = 0, k-1, i!) + 1);

Extensions

a(14)-a(16) from Michael S. Branicky, Oct 03 2024