A147952 a(0) = 0, a(1) = a(2) = 1, and for n >= 3, a(n) = a(a(n-2)) + r(n), where r(n) = a(a(floor(n/3))) when n == 0 or 1 (mod 3) and = a(n - a(floor(n/3))) when n == 2 (mod 3).

0, 1, 1, 2, 2, 3, 2, 3, 4, 3, 3, 5, 3, 4, 5, 4, 5, 7, 4, 4, 6, 4, 4, 8, 4, 6, 6, 4, 4, 8, 4, 6, 10, 5, 6, 7, 4, 5, 9, 5, 5, 8, 6, 7, 7, 5, 5, 10, 6, 6, 7, 5, 6, 8, 4, 6, 8, 4, 6, 8, 4, 6, 10, 4, 5, 8, 5, 6, 8, 6, 8, 6, 6, 4, 10, 4, 5, 8, 5, 6, 13, 4, 6, 8, 4, 6, 8, 6, 8, 6, 6, 4, 10, 4, 5, 8, 6, 7, 10, 6, 6

Offset: 0

Author

Roger L. Bagula, Nov 17 2008

Keywords

• nonn

Crossrefs

Cf. A147665, A147953, A147981.

Programs

Mathematica

f[0] = 0; f[1] = 1; f[2] = 1; f[n_] := f[n] = f[f[n - 2]] + If[Mod[n, 3] == 0,f[f[n/3]], If[Mod[n, 3] == 1, f[f[(n - 1)/3]], f[n - f[(n - 2)/3]]]]; Table[f[n], {n, 0, 100}]

Formula

a(n) = a(a(n - 2)) + If[Mod[n, 3] == 0, a(a(n/3)), If[Mod[n, 3] == 1, a(a((n - 1)/3)), a(n - a((n - 2)/3))] for n >= 3 with a(0) = 0 and a(1) = a(2) = 1. [edited by Petros Hadjicostas, Apr 13 2020]

Extensions

Name edited by Petros Hadjicostas, Apr 13 2020