A112853 Numbers k such that (2*k)!/k!-1 is prime.

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

Offset: 1

Author

Hugo Pfoertner, Sep 25 2005

Keywords

• hard
• more
• nonn

Comments

Next term is > 9680.

Crossrefs

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.

Programs

Mathematica

Select[Range[7000], PrimeQ[(2#)!/#!-1]&] (* James C. McMahon, Jun 12 2024 *)

Extensions

a(15) from Michael S. Branicky, Jun 12 2024