A112861 Numbers k such that (2*k)!/(2*(k!)^2) - 1 is prime.

2, 6, 10, 21, 45, 63, 306, 404, 437, 471, 646, 1174, 1192, 1334, 1975, 2397, 2410, 4305, 6111, 7852, 9488, 11120, 13304, 14408, 16075, 16238, 21188, 21659, 22025, 28673, 30793, 32178, 35278, 40049, 46516, 47836, 52157, 54531, 59897, 60275, 63362, 76139, 84219, 89024, 90783, 91605, 96761

Offset: 1

Author

Hugo Pfoertner, Sep 30 2005

Keywords

• hard
• nonn

Comments

a(48) > 100000. - Robert Price, Jul 25 2024

Crossrefs

Cf. A001700(n-1) = (2*n)!/(2*(n!)^2); A112862: primes of the form (2*n)!/(2*(n!)^2)-1; A112853: (2*n)!/n!-1 is prime; A112855: (2*n)!/n!+1 is prime; A066726: (2*n)!/(n!)^2-1 is prime; A066699: (2*n)!/(n!)^2+1 is prime; A112863: (2*n)!/(2*(n!)^2)+1 is prime.

Programs

Magma

[n: n in [1..700] | IsPrime(Factorial(2*n) div (2*Factorial(n)^2)-1)]; // Vincenzo Librandi, Apr 10 2015

Mathematica

Select[Range[10000], PrimeQ[(2 #)! / (2 (#!)^2) - 1 ] &] (* Vincenzo Librandi, Apr 10 2015 *)

Extensions

a(22)-a(26) from Vaclav Kotesovec, May 02 2021

a(27)-a(47) from Robert Price, Jul 25 2024