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

1,1

Comments

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

Links

Table of n, a(n) for n=1..47.

Mathematica

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

Prog

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

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.

Sequence in context: A297185 A372452 A304991 * A180230 A186296 A140775

Adjacent sequences: A112858 A112859 A112860 * A112862 A112863 A112864

Keyword

hard,nonn

Author

Hugo Pfoertner, Sep 30 2005

Extensions

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

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

Status

approved