A066699 Numbers k such that binomial(2k,k)+1 is prime.

1, 2, 4, 7, 12, 19, 22, 38, 46, 62, 68, 72, 84, 166, 184, 214, 340, 348, 445, 517, 692, 817, 1316, 1381, 2554, 2713, 5261, 6209, 6735, 7920, 8207, 8772, 9530, 13075, 13302, 13405, 15002, 16371, 19346, 24151, 26555, 28188, 29235, 33536, 43338, 44048, 65576, 65930, 68666, 78285

Offset: 1

Author

Joseph L. Pe, Jan 14 2002

Keywords

• nonn

Comments

a(45) > 40000. All the primes corresponding to terms up to a(44) have been certified by the PFGW software performing the Brillhart-Lehmer-Selfridge N-1 test. - Giovanni Resta, Apr 05 2017

a(51) > 100000. - Robert Price, Jul 02 2024

Examples

			C(4,2) + 1 = 7, a prime; so 2 is a term of the sequence.
		

References

• Aigner and Ziegler. Proofs from the Book, 2nd edition. Springer-Verlag, 2001.

Crossrefs

Cf. A085793, A066726.

Programs

Mathematica

Do[If[PrimeQ[Binomial[2 a, a]+1], a >>>"C:\prime.txt"],{a,1,20000}] (* Ed Pegg Jr *)
Select[Range[1, 5 * 10^2], PrimeQ[Binomial[2* #, # ] + 1] &]

PARI

is(n)=isprime(binomial(2n,n)+1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms (not certified primes) from Jason Earls and Robert G. Wilson v, Jan 15 2002

More terms from Ed Pegg Jr, Sep 10 2003

a(40)-a(44) from Giovanni Resta, Apr 05 2017

a(45)-a(50) from Robert Price, Jul 02 2024