A107757 Numbers k such that Sum_{j=1..k} Catalan(j) == 2 (mod 3).

3, 9, 11, 27, 29, 35, 39, 81, 83, 89, 93, 107, 111, 117, 119, 243, 245, 251, 255, 269, 273, 279, 281, 323, 327, 333, 335, 351, 353, 359, 363, 729, 731, 737, 741, 755, 759, 765, 767, 809, 813, 819, 821, 837, 839, 845, 849, 971, 975, 981, 983, 999, 1001, 1007, 1011

Offset: 1

Author

N. J. A. Sloane, Jun 11 2005

Keywords

• nonn
• easy

Links

• Y. More, Problem 11165, Amer. Math. Monthly, 112 (2005), 568.

Crossrefs

Cf. A000108, A107755, A107756.

Equals A074939 - 1.

Programs

Maple

c:=n->binomial(2*n,n)/(n+1): s:=0: for n from 1 to 1500 do s:=s+c(n): a[n]:=s mod 3: od: A:=[seq(a[n],n=1..1500)]: p:=proc(n) if A[n]=2 then n else fi end: seq(p(n),n=1..1500); # Emeric Deutsch, Jun 12 2005

Mathematica

s0 = s2 = {}; s = 0; Do[s = Mod[s + (2 n)!/n!/(n + 1)!, 3]; Switch[ Mod[s, 3], 0, AppendTo[s0, n], 2, AppendTo[s2, n]], {n, 1055}]; s2 (* Robert G. Wilson v, Jun 14 2005 *)

Extensions

More terms from Emeric Deutsch, Jun 12 2005