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

1,1

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

Links

Table of n, a(n) for n=1..54.

Mathematica

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

Prog

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

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

Sequence in context: A167510 A351359 A191701 * A124642 A370641 A269153

Adjacent sequences: A066723 A066724 A066725 * A066727 A066728 A066729

Keyword

nonn

Author

Robert G. Wilson v, Jan 15 2002

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

Status

approved