A372903 Numbers k that divide the k-th little Schroeder number.

1, 33, 2295, 5439, 6699, 7095, 7497, 7595, 10241, 11475, 15345, 19845, 24651, 25245, 35845, 37725, 37791, 49203, 50463, 51183, 51471, 60291, 62073, 64337, 65569, 66495, 68313, 78793, 80223, 81809, 86031, 98167, 100659, 103293, 109395, 115245, 119067, 119919, 142137

Offset

1,2

Comments

Numbers k such that k | A001003(k).

Links

Amiram Eldar, Table of n, a(n) for n = 1..208

Example

1 is a term since A001003(1) = 2 is divisible by 1.
33 is a term since A001003(33) = 37836272668898230450209 = 33 * 1146553717239340316673 is divisible by 33.

Mathematica

seq[kmax_] := Module[{sc0 = 1, sc1 = 1, sc2, s = {1}}, Do[sc2 = ((6*k-3)*sc1 - (k-2)*sc0)/(k+1); If[Divisible[sc2, k], AppendTo[s, k]]; sc0 = sc1; sc1 = sc2, {k, 2, kmax}]; s]; seq[10^5]

Prog

(PARI) lista(kmax) = {my(sc0 = 1, sc1 = 1, sc2); print1(1, ", "); for(k = 2, kmax, sc2 = ((6*k-3)*sc1 - (k-2)*sc0)/(k+1); if(!(sc2 % k), print1(k, ", ")); sc0 = sc1; sc1 = sc2); }

Crossrefs

Cf. A001003.

Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).

Sequence in context: A380638 A294611 A294954 * A118641 A263908 A358808

Adjacent sequences: A372900 A372901 A372902 * A372904 A372905 A372906

Keyword

nonn

Author

Amiram Eldar, May 16 2024

Status

approved