A112863 Numbers k such that (2*k)!/(2*(k!)^2)+1 is prime.
1, 3, 5, 6, 14, 19, 24, 45, 49, 62, 72, 122, 149, 197, 209, 222, 349, 409, 491, 527, 601, 675, 728, 769, 795, 853, 1039, 1318, 1599, 2069, 2279, 2567, 2634, 3286, 3482, 6880, 6919, 9117, 9276, 9564, 10898, 13061, 14570, 16493, 17366, 18773, 19901, 25569, 26611, 28322
Offset: 1
Programs
-
Mathematica
Select[Range[3000],PrimeQ[(2#)!/(2(#!)^2)+1]&] (* James C. McMahon, Jun 13 2024 *)
-
PARI
isok(k) = ispseudoprime(1+binomial(2*k-1, k-1)); \\ Michel Marcus, Jun 14 2024
Extensions
a(42)-a(43) from Charles R Greathouse IV, Sep 26 2006
a(44)-a(50) from Michael S. Branicky, Jul 24 2024