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

1,2

Links

Table of n, a(n) for n=1..73.

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

Formula

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

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 *)

Crossrefs

Cf. A000108, A107755, A107757.

Equals A074940 - 1.

Sequence in context: A123438 A039024 A065028 * A080723 A288737 A139448

Adjacent sequences: A107753 A107754 A107755 * A107757 A107758 A107759

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 11 2005

Status

approved