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

1, 2, 7, 13, 23, 5666

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..6.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A118812 (corresponding primes).

Sequence in context: A366983 A045377 A180470 * A182415 A275491 A360673

Adjacent sequences: A237440 A237441 A237442 * A237444 A237445 A237446

Keyword

nonn,hard,more

Author

Rick L. Shepherd, Feb 07 2014

Extensions

a(6) from Michal Paulovic, Nov 22 2023

Status

approved