A066726 Numbers n such that binomial(2n, n) - 1 is prime.

2, 3, 5, 9, 15, 29, 43, 51, 113, 184, 213, 222, 267, 279, 369, 402, 441, 603, 812, 839, 902, 1422, 1542, 1824, 2983, 3065, 3911, 3958, 4192, 4587, 4865, 5543, 5837, 7902, 9299, 9722, 10412, 10648, 11498, 12803, 14428, 15876, 20173, 26311, 38927, 52210, 54189, 59757, 60454, 72094, 76899, 85033, 91059, 91059

Offset: 1

Author

Robert G. Wilson v, Jan 15 2002

Keywords

• nonn

Comments

I.e., numbers n such that (2*n)!/(n!)^2-1 is prime. - Hugo Pfoertner, Sep 25 2005

The next term is > 30000. - Vaclav Kotesovec, May 03 2021

a(55) > 100000. - Robert Price, Jul 02 2024

Crossrefs

Cf. A066699, A085793.

Cf. A092751 = primes of the form (2*n)!/(n!)^2-1, A112853 = (2*n)!/n!-1 is prime, A112855 = (2*n)!/n!+1 is prime, A066699 = (2*n)!/(n!)^2+1 is prime, A112861 = (2*n)!/(2*(n!)^2)-1 is prime, A112863 = (2*n)!/(2*(n!)^2)+1 is prime. - Hugo Pfoertner, Sep 25 2005

Programs

Mathematica

Do[ If[ PrimeQ[ Binomial[2n, n] - 1], Print[n]], {n, 1, 2000} ]

PARI

is(n)=isprime(binomial(2*n,n)-1) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

More terms from Ed Pegg Jr, Sep 10 2003

Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar

a(43)-a(44) from Vaclav Kotesovec, May 03 2021

a(45)-a(54) from Robert Price, Jul 02 2024