A121852 Numbers n such that partial sum of Catalan numbers A014137(n) is a prime.

1, 4, 6, 16, 24, 104, 121, 283, 326, 489, 1387, 1394, 1424, 1435, 1985, 4323, 5221

Offset: 1

Author

Alexander Adamchuk, Aug 30 2006

Keywords

• hard
• nonn

Comments

Corresponding primes are A014137( a(n)) = {2,23,197,48760367,1757900019101,...}.

Examples

			Catalan numbers A000108(n) begin {1,1,2,5,14,42,132,429,1430,4862,...}.
a(1) = 1 because A014137(1) = 1 + 1 = 2 is prime,
a(2) = 4 because A014137(4) = 1 + 1 + 2 + 5 + 14 = 23 is prime.
		

Crossrefs

Cf. A000108, A014137.

Programs

Mathematica

s = 1; Do[s = s + (2n)!/((n!)^2(n + 1)); If[PrimeQ@s, Print@n], {n, 17925}] (* Robert G. Wilson v *)

Extensions

a(11) - a(17) from Robert G. Wilson v, Aug 31 2006