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

0,4

Links

Table of n, a(n) for n=0..86.

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}]

Crossrefs

Cf. A004001, A147665, A147955.

Sequence in context: A226390 A156081 A368991 * A105047 A331135 A089881

Adjacent sequences: A147951 A147952 A147953 * A147955 A147956 A147957

Keyword

nonn

Author

Roger L. Bagula, Nov 17 2008

Extensions

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

Status

approved