A126807 Numbers k such that A014138(k+1) (the partial sum of the first k Catalan numbers, starting 1, 2, 5, ...) is a prime.

1, 8, 10, 30, 45, 145, 794, 2772, 2787, 9796, 38288, 39191, 40856, 41202, 47379

Offset: 1

Author

Alexander Adamchuk, Feb 23 2007

Keywords

• more
• nonn

Comments

a(16) > 156000. - Michael S. Branicky, Jun 26 2025

Crossrefs

Cf. A014138, A000108, A134775.

Cf. A014137, A121852 (sum of first k Catalan numbers A014137(k) is prime).

Programs

Maple

s[0]:=1: for n to 1000 do s[n]:= s[n-1]+binomial(2*n+2, n+1)/(n+2) end do: a:= proc (n) if isprime(s[n]) = true then n else end if end proc: seq(a(n), n= 0.. 1000); # Emeric Deutsch, Aug 28 2007

Mathematica

s = 0; Do[s = s + (2n)!/n!/(n+1)!; If[ PrimeQ[s], Print[n-1]], {n, 200}]

Formula

a(n) = A134775(n) - 1. - Michael S. Branicky, Jun 24 2025

Extensions

a(7)-a(9) from Emeric Deutsch, Aug 28 2007

Name clarified by Jon E. Schoenfield, Mar 25 2019

a(10)-a(15) from Michael S. Branicky, Jun 25 2025