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

1,2

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

References

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

Links

Table of n, a(n) for n=1..50.

Example

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

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] &]

Prog

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

Crossrefs

Cf. A085793, A066726.

Sequence in context: A105807 A209616 A192521 * A188425 A087149 A090853

Adjacent sequences: A066696 A066697 A066698 * A066700 A066701 A066702

Keyword

nonn

Author

Joseph L. Pe, Jan 14 2002

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

Status

approved