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A112861 Numbers n such that (2*n)!/(2*(n!)^2) - 1 is prime. 6
2, 6, 10, 21, 45, 63, 306, 404, 437, 471, 646, 1174, 1192, 1334, 1975, 2397, 2410, 4305, 6111, 7852, 9488 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The next term is > 11000.

LINKS

Table of n, a(n) for n=1..21.

MATHEMATICA

lst={}; Do[If[PrimeQ[(2*n)!/(2*(n!)^2)-1], AppendTo[lst, n]], {n, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)

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; A112859: (2*n)!/(n!)^2+1 is prime; A112863: (2*n)!/(2*(n!)^2)+1 is prime.

Sequence in context: A034450 A297185 A304991 * A180230 A186296 A140775

Adjacent sequences:  A112858 A112859 A112860 * A112862 A112863 A112864

KEYWORD

hard,nonn

AUTHOR

Hugo Pfoertner, Sep 30 2005

STATUS

approved

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Last modified July 17 18:43 EDT 2019. Contains 325109 sequences. (Running on oeis4.)