A107756 Numbers k such that Sum_{j=1..k} Catalan(j) == 1 (mod 3).

1, 4, 5, 6, 7, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 31, 32, 33, 34, 37, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82, 85, 86, 87, 88, 91, 94, 95

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, A107757.

Equals A074940 - 1.

Programs

Mathematica

Select[ Range[ 100], Mod[ Sum[(2 n)!/n!/(n + 1)!, {n, #}], 3] == 1 &] (* Robert G. Wilson v, Jun 14 2005 *)
Position[Accumulate[CatalanNumber[Range[100]]],?(Mod[#,3]==1&)]//Flatten (* _Harvey P. Dale, Aug 26 2022 *)

Formula

Equivalently, numbers k such that base-3 expansion of k+1 contains a 2.