A317223 a(0) = 0, a(1) = 1; for n >= 2, a(n) = freq(a(freq(a(n-1),n)),n) where 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, 2, 4, 2, 5, 2, 1, 6, 3, 3, 6, 3, 6, 6, 6, 6, 4, 3, 6, 6, 2, 7, 3, 6, 7, 3, 7, 7, 7, 7, 7, 7, 2, 2, 9, 3, 2, 1, 10, 4, 10, 4, 10, 10, 10, 10, 8, 4, 10, 10, 5, 4, 8, 4, 10, 10, 2, 11, 4, 8, 11, 4, 11, 11, 11, 11, 8, 11, 11, 9, 4, 2, 4, 12, 4, 4, 9, 12, 4, 8, 12, 12, 12, 12, 8, 8, 12, 12, 14, 4, 8

Offset: 0

Author

Altug Alkan, Jul 24 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..65536
• Alois P. Heinz, Log plot of n, a(n) for n = 0..2^20

Crossrefs

Cf. A316774, A317015, A317127.

Programs

Maple

b:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= `if`(n<2, n, b(a(b(a(n-1)))));
      b(t):= b(t)+1; t
    end:
seq(a(n), n=0..200);  # Alois P. Heinz, Jul 24 2018

Mathematica

b[_] = 0;
a[n_] := a[n] = Module[{t}, t = If[n<2, n, b[a[b[a[n-1]]]]]; b[t]++; t];
a /@ Range[0, 200] (* Jean-François Alcover, Nov 09 2020, after Alois P. Heinz *)