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%I #28 Feb 17 2024 12:23:27
%S 1,2,7,13,23,5666
%N Numbers m such that (2m)! - m! + 1 is prime.
%C If it exists, a(7) > 7*10^3. - _Michal Paulovic_, Feb 17 2024
%e 2 is in the sequence because 4! - 2! + 1 = 23 is prime.
%e 7 is in the sequence because 14! - 7! + 1 = 87178286161 is prime.
%e 12 is not in the sequence because 24! - 12! + 1 = 620448401733238960358401 = 587 * 21523 * 49109415278124401.
%t Select[Range[100], PrimeQ[(2#)! - #! + 1] &] (* _Alonso del Arte_, Feb 09 2014 *)
%o (PARI) for(n = 1, 2500, if(isprime((2*n)! - n! + 1), print1(n, ", ")))
%Y Cf. A118812 (corresponding primes).
%K nonn,hard,more
%O 1,2
%A _Rick L. Shepherd_, Feb 07 2014
%E a(6) from _Michal Paulovic_, Nov 22 2023
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