A317359 a(0) = 0, a(1) = 1; for n >= 2, a(n) = freq(a(n-g(n)),n) where g = A000523 and freq(i, j) is the number of times i appears in the terms a(0) .. a(j-1).

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 8, 8, 8, 8, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 4, 12, 12, 12, 12, 12, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 11, 11, 11, 11, 11, 5, 5, 5, 5, 5, 5, 17, 17, 17, 17, 17, 17, 6, 6, 6, 6, 6, 6, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 11, 11, 11, 11, 11

Offset: 0

Author

Altug Alkan, Jul 26 2018

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..65536
• Altug Alkan, A line graph of a(n) for n <= 2500

Crossrefs

Cf. A000523, A317223, A317361.

Programs

Maple

b:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= `if`(n<2, n, b(a(n-ilog2(n))));
      b(t):= b(t)+1; t
    end:
seq(a(n), n=0..200);  # Alois P. Heinz, Jul 26 2018

Mathematica

c = <||>; f[n_] := If[KeyExistsQ[c, n], c[n], 0]; a[n_] := a[n] = Block[{v}, v = If[n < 2, n, f[a[n - Floor@ Log2@ n]]]; If[f[v] > 0, c[v] = c[v] + 1, c[v] = 1]; v]; Array[a, 96, 0] (* Giovanni Resta, Jul 26 2018 *)