%I #22 Aug 14 2024 02:14:26
%S 0,12,43,53,120,121,184,778,823,1179,1212,1670,3187,3353,4282,5420,
%T 5592,5826,6526,7405,7581,7619,13213,17258,17532,17644,20274,24404,
%U 40406,41981,46955,52968,52968,64289,77776,82571,91231,99641
%N Numbers k such that binomial(3k, k) + 1 is prime.
%C a(39) > 10^5. - _Robert Price_, Aug 13 2024
%t Do[f=Binomial[3n,n]+1;If[PrimeQ[f],Print[n]],{n,1,1000}]
%o (PARI) is(n)=isprime(binomial(3*n,n)+1) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A125220, A066699, A066726.
%K hard,more,nonn
%O 1,2
%A _Alexander Adamchuk_, Nov 24 2006
%E a(10)-a(15) from _Robert G. Wilson v_, Nov 26 2006
%E More terms from _Stefan Steinerberger_, Sep 07 2007
%E 5 more terms from _Ryan Propper_, Jan 01 2008
%E a(24)-a(31) from _Robert Price_, Apr 17 2019
%E a(32)-a(38) from _Robert Price_, Aug 13 2024