A085793 Numbers k such that (k-1)*binomial(2k,k) + 1 is prime.

2, 3, 4, 5, 6, 7, 9, 13, 17, 18, 22, 23, 28, 31, 48, 49, 52, 80, 99, 167, 201, 295, 372, 381, 391, 638, 653, 720, 779, 887, 1047, 1454, 1647, 1719, 2405, 3234, 3257, 3542, 3623, 3765, 3796, 4337, 4490, 5228, 6507, 8544, 9990, 10000, 12478, 13479, 15487, 17115

Offset: 1

Author

Ed Pegg Jr, Jul 23 2003

Keywords

• nonn

Comments

a(69) > 10^5 - Robert Price, Sep 15 2024

Examples

			9999 * 20000!/(10000!)^2 + 1 is prime
		

Links

• Robert Price, Table of n, a(n) for n = 1..68
• Ed Pegg Jr, Binomial Primes.

Crossrefs

Cf. A066699, A066726.

Programs

PARI

is(n)=ispseudoprime((n-1)*binomial(2*n,n)+1) \\ Charles R Greathouse IV, May 22 2017

Extensions

a(53)-a(68) from Robert Price, Sep 15 2024