A125220 Numbers k such that binomial(3k, k) - 1 is prime.

1, 3, 7, 11, 49, 88, 93, 196, 216, 519, 655, 722, 858, 905, 991, 1654, 2277, 3275, 4214, 5047, 5924, 7359, 7953, 11188, 13286, 14626, 14687, 34365, 36014, 65613, 93663, 101805

Offset: 1

Author

Alexander Adamchuk, Nov 25 2006

Keywords

• hard
• more
• nonn

Crossrefs

Cf. A125221 (binomial(3k, k) + 1 is prime).

Cf. A066699 (binomial(2k, k) + 1 is prime).

Cf. A066726 (binomial(2k, k) - 1 is prime).

Programs

Mathematica

Do[f=Binomial[3n, n]-1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]
Select[Range[4300],PrimeQ[Binomial[3#,#]-1]&] (* Harvey P. Dale, Aug 24 2017 *)

PARI

is(n)=binomial(3*n,n)-1 \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(16)-a(19) from Robert G. Wilson v, Nov 26 2006

a(20)-a(29) from Robert Price, Apr 23 2019

a(30)-a(32) from Georg Grasegger, May 26 2025