|
|
A112861
|
|
Numbers k such that (2*k)!/(2*(k!)^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, 11120, 13304, 14408, 16075, 16238
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
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.
|
|
KEYWORD
|
hard,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|