A125242 Numbers k such that binomial(5k, k) - 1 is prime.

5, 71, 111, 187, 239, 247, 473, 628, 847, 1478, 2687, 3530, 5175, 9113, 10968, 15039, 28929, 35649, 43481, 44455, 51269, 63975, 71723

Offset: 1

Author

Alexander Adamchuk, Nov 25 2006

Keywords

• hard
• more
• nonn

Comments

a(24) > 10^5. Robert Price, Nov 16 2024

Crossrefs

Cf. A125243 = numbers n such that binomial(5n, 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, A125240, A125241, A125244, A125245.

Programs

Mathematica

Do[f=Binomial[5n, n]-1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]
Select[Range[45000],PrimeQ[Binomial[5#,#]-1]&] (* Harvey P. Dale, Jan 02 2022 *)

Extensions

More terms from Ryan Propper, Jan 06 2007

a(15)-a(20) from Robert Price, May 03 2019

a(21)-a(23) from Robert Price, Nov 16 2024