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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).

%I A317359 #15 Jul 26 2018 17:59:18
%S A317359 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,
%T A317359 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,
%U A317359 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
%N 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).
%H A317359 Alois P. Heinz, <a href="/A317359/b317359.txt">Table of n, a(n) for n = 0..65536</a>
%H A317359 Altug Alkan, <a href="/A317359/a317359.png">A line graph of a(n) for n <= 2500</a>
%p A317359 b:= proc() 0 end:
%p A317359 a:= proc(n) option remember; local t;
%p A317359       t:= `if`(n<2, n, b(a(n-ilog2(n))));
%p A317359       b(t):= b(t)+1; t
%p A317359     end:
%p A317359 seq(a(n), n=0..200);  # _Alois P. Heinz_, Jul 26 2018
%t A317359 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 *)
%Y A317359 Cf. A000523, A317223, A317361.
%K A317359 nonn,look
%O A317359 0,4
%A A317359 _Altug Alkan_, Jul 26 2018