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%I #15 Dec 15 2017 17:35:48
%S 1,2,4,7,12,19,22,38,46,62,68,72,84,166,184,214,340,348,445,517,692,
%T 817,1316,1381,2554,2713,5261,6209,6735,7920,8207,8772,9530,13075,
%U 13302,13405,15002,16371,19346,24151,26555,28188,29235,33536
%N Numbers n such that binomial(2n,n)+1 is prime.
%C 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
%D Aigner and Ziegler. Proofs from the Book, 2nd edition. Springer-Verlag, 2001.
%e C(4,2) + 1 = 7, a prime; so 2 is a term of the sequence.
%t Do[If[PrimeQ[Binomial[2 a, a]+1], a >>>"C:\prime.txt"],{a,1,20000}] (* _Ed Pegg Jr_ *)
%t Select[Range[1, 5 * 10^2], PrimeQ[Binomial[2* #, # ] + 1] &]
%o (PARI) is(n)=isprime(binomial(2n,n)+1) \\ _Charles R Greathouse IV_, May 15 2013
%Y Cf. A085793, A066726.
%K nonn
%O 1,2
%A _Joseph L. Pe_, Jan 14 2002
%E More terms (not certified primes) from _Jason Earls_ and _Robert G. Wilson v_, Jan 15 2002
%E More terms from _Ed Pegg Jr_, Sep 10 2003
%E a(40)-a(44) from _Giovanni Resta_, Apr 05 2017
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