A133927 Numbers k such that the sum of the first k Catalan numbers, C_1 + C_2 + ... + C_k, is divisible by k.

1, 30, 494, 6331, 36851, 95450, 122614, 940745, 5126032, 7519204

Offset: 1

Author

Ryan Propper, Jan 07 2008

Keywords

• hard
• more
• nonn

Comments

The sum of the first 30 Catalan numbers, 1 + 2 + 5 + ... + 3814986502092304 = 5175497420902740, is divisible by 30, so 30 is a term.

No more terms < 5*10^7. - Lars Blomberg, Nov 07 2011

Links

• Eric Weisstein's World of Mathematics, Catalan Number

Crossrefs

Cf. A000108, A014138.

Programs

Mathematica

Module[{nn=40000,lst},lst=Thread[{Range[nn],Accumulate[CatalanNumber[Range[nn]]]}]; Position[ lst,?(Mod[#[[2]],#[[1]]]==0&),1,Heads->False]]//Flatten (* The program generates the first 5 terms of the sequence. *) (* _Harvey P. Dale, Jun 18 2024 *)