A112853 - OEIS

%I #15 Jun 13 2024 09:43:49

%S 2,6,14,25,114,188,193,361,712,1767,3195,4995,5682,6485,9937

%N Numbers k such that (2*k)!/k!-1 is prime.

%C Next term is > 9680.

%t Select[Range[7000], PrimeQ[(2#)!/#!-1]&] (* _James C. McMahon_, Jun 12 2024 *)

%Y Cf. A112854 primes of the form (2*n)!/n!-1, A112855 (2*n)!/n!+1 is prime, A066726 (2*n)!/(n!)^2-1 is prime, A066699 (2*n)!/(n!)^2+1 is prime, A112861 (2*n)!/(2*(n!)^2)-1 is prime, A112863 (2*n)!/(2*(n!)^2)+1 is prime.

%K hard,more,nonn

%O 1,1

%A _Hugo Pfoertner_, Sep 25 2005

%E a(15) from _Michael S. Branicky_, Jun 12 2024