A125241 Numbers k such that binomial(4k, k) + 1 is prime.

0, 1, 2, 6, 10, 11, 19, 28, 80, 123, 141, 147, 154, 198, 200, 346, 851, 887, 1038, 1329, 2045, 3228, 3274, 3588, 6794, 8045, 11911, 12184, 12327, 12515, 20089, 38173, 41026, 48914, 71772, 72130, 100726

Offset: 1

Author

Alexander Adamchuk, Nov 25 2006

Keywords

• hard
• more
• nonn

Crossrefs

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.

Programs

Mathematica

Do[f=Binomial[4n, n]+1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]
Select[Range[8100],PrimeQ[Binomial[4#,#]+1]&] (* Harvey P. Dale, Aug 24 2014 *)

Extensions

More terms from Ryan Propper, Mar 28 2007

a(1)=0 added by Robert Price, May 01 2019

a(27)-a(34) from Robert Price, May 01 2019

a(35)-a(37) from Georg Grasegger, Jun 02 2025