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Numbers k such that binomial(4k, k) - 1 is prime.
5

%I #12 Sep 15 2024 14:40:37

%S 1,16,36,67,95,369,383,745,1599,2006,2104,2879,3061,9048,9902,12369,

%T 15058,18858,21287,22759,24674,33899,43730,55078,86085

%N Numbers k such that binomial(4k, k) - 1 is prime.

%C a(26) > 10^5 - _Robert Price_, Sep 15 2024

%t Do[f=Binomial[4n, n]-1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]

%Y Cf. A125241 = 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 1,2

%A _Alexander Adamchuk_, Nov 25 2006

%E More terms from _Ryan Propper_, Mar 28 2007

%E a(16)-a(23) from _Robert Price_, Apr 30 2019

%E a(24)-a(25) from _Robert Price_, Sep 15 2024