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%I #10 May 01 2019 10:20:39
%S 0,1,2,6,10,11,19,28,80,123,141,147,154,198,200,346,851,887,1038,1329,
%T 2045,3228,3274,3588,6794,8045,11911,12184,12327,12515,20089,38173,
%U 41026,48914
%N Numbers k such that binomial(4k, k) + 1 is prime.
%t Do[f=Binomial[4n, n]+1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]
%t Select[Range[8100],PrimeQ[Binomial[4#,#]+1]&] (* _Harvey P. Dale_, Aug 24 2014 *)
%Y Cf. A125240 = numbers n such that binomial(4n, n) - 1 is prime. Cf. A066699 = numbers n such that binomial(2n, n) + 1 is prime. Cf. A066726 = numbers n such that binomial(2n, n) - 1 is prime. Cf. A125220, A125221, A125242, A125243, A125244, A125245.
%K hard,more,nonn
%O 1,3
%A _Alexander Adamchuk_, Nov 25 2006
%E More terms from _Ryan Propper_, Mar 28 2007
%E a(1)=0 added by _Robert Price_, May 01 2019
%E a(27)-a(34) from _Robert Price_, May 01 2019