A147665 a(n) = a(a(n - 1)) + r(n) for n >= 3, where r(3*k) = a(a(k)), r(3*k+1) = a(a(k)) and r(3*k+2) = a(n-a(k)), with a(0) = 0 and a(1) = a(2) = 1.

0, 1, 1, 2, 2, 3, 3, 3, 5, 4, 3, 6, 4, 3, 6, 5, 5, 9, 6, 5, 12, 6, 5, 15, 8, 8, 11, 8, 7, 11, 8, 7, 14, 9, 7, 14, 8, 7, 10, 5, 5, 13, 6, 6, 13, 6, 6, 9, 7, 6, 9, 8, 9, 17, 12, 7, 12, 7, 6, 15, 9, 8, 14, 9, 7, 18, 9, 7, 12, 9, 9, 16, 10, 8, 14, 11, 11, 15, 11, 12, 13, 8, 10, 14, 9, 7, 15, 11, 12, 15

Offset: 0

Author

Roger L. Bagula, Nov 09 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A004001, A140473, A143089, A143091, A147871.

Programs

Mathematica

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

Python

def A147665(n):
    if n <= 2: return [0, 1, 1][n]
    elif n % 3 <= 1: return A147665(A147665(n-1)) + A147665(A147665(n//3))
    else: return A147665(A147665(n-1)) + A147665(n - A147665(n//3))
print([A147665(n) for n in range(100)]) # Oct 18 2009

Formula

a(n) = a(a(n - 1)) + r(n) for n >= 3, where r(3*k) = a(a(k)), r(3*k+1) = a(a(k)) and r(3*k+2) = a(n-a(k)), with a(0) = 0 and a(1) = a(2) = 1.

Extensions

Applied OEIS standards to nomenclature - The Assoc. Editors of the OEIS, Oct 18 2009

Name edited by Petros Hadjicostas, Apr 11 2020