A147954 a(0) = 0, a(1) = a(2) = 1, a(n) = a(a(n-1)) + a(n-a(n-1)) for 3 <= n <= 5, and a(n) = a(a(n-1)) + r(n) for n >= 6, where r(n) = a(a(floor(n/6))) for n == 0, 1, 2, 3, 4 (mod 6), and r(n) = a(n - a(floor(n/6))) for n == 5 (mod 6).

0, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 5, 4, 3, 3, 3, 3, 5, 4, 3, 3, 3, 3, 5, 4, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 8, 6, 6, 6, 6, 6, 9, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 8, 5, 5, 5

Offset: 0

Author

Roger L. Bagula, Nov 17 2008

Keywords

• nonn

Crossrefs

Cf. A004001, A147665, A147955.

Programs

Maple

a := proc(n) local v; option remember;
if n = 0 then v := 0; end if;
if n = 1 or n = 2 then v := 1; end if;
if 3 <= n and n <= 5 then v := a(a(n - 1)) + a(n - a(n - 1)); end if;
if 6 <= n and 5 <> n mod 6 then v := a(a(n - 1)) + a(a(floor(n/6))); end if;
if 6 <= n and 5 = n mod 6 then v := a(a(n - 1)) + a(n - a(floor(n/6))); end if; v; end proc; # Petros Hadjicostas, Apr 21 2020

Mathematica

f[0] = 0; f[1] = 1; f[2] = 1;
f[n_] := f[n] =
  f[f[n - 1]] +
   If[n < 6, f[n - f[n - 1]],
    If[Mod[n, 6] == 0, f[f[n/6]],
     If[Mod[n, 6] == 1, f[f[(n - 1)/6]],
      If[Mod[n, 6] == 2, f[f[(n - 2)/6]],
       If[Mod[n, 6] == 3, f[f[(n - 3)/6]],
        If[Mod[n, 6] == 4, f[f[(n - 4)/6]], f[n - f[(n - 5)/6]]]]]]]];
Table[f[n], {n, 0, 300}]

Extensions

Name, data, and Mathematica program edited and corrected by Petros Hadjicostas, Apr 21 2020