A237443 Numbers m such that (2m)! - m! + 1 is prime.

1, 2, 7, 13, 23, 5666, 32918

Offset: 1

Author

Rick L. Shepherd, Feb 07 2014

Keywords

• nonn
• hard
• more

Comments

If it exists, a(7) > 7*10^3. - Michal Paulovic, Feb 17 2024

If it exists, a(8) > 6*10^4. - Kellen Shenton, Dec 21 2024

Examples

			2 is in the sequence because 4! - 2! + 1 = 23 is prime.
7 is in the sequence because 14! - 7! + 1 = 87178286161 is prime.
12 is not in the sequence because 24! - 12! + 1 = 620448401733238960358401 = 587 * 21523 * 49109415278124401.
		

Crossrefs

Cf. A118812 (corresponding primes).

Programs

Mathematica

Select[Range[100], PrimeQ[(2#)! - #! + 1] &] (* Alonso del Arte, Feb 09 2014 *)

PARI

for(n = 1, 2500, if(isprime((2*n)! - n! + 1), print1(n, ", ")))

Extensions

a(6) from Michal Paulovic, Nov 22 2023

a(7) from Kellen Shenton, Dec 21 2024