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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).

%I A317223 #16 Nov 09 2020 02:55:47
%S A317223 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,
%T A317223 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,
%U A317223 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
%N 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).
%H A317223 Alois P. Heinz, <a href="/A317223/b317223.txt">Table of n, a(n) for n = 0..65536</a>
%H A317223 Alois P. Heinz, <a href="/A317223/a317223.jpg">Log plot of n, a(n) for n = 0..2^20</a>
%p A317223 b:= proc() 0 end:
%p A317223 a:= proc(n) option remember; local t;
%p A317223       t:= `if`(n<2, n, b(a(b(a(n-1)))));
%p A317223       b(t):= b(t)+1; t
%p A317223     end:
%p A317223 seq(a(n), n=0..200);  # _Alois P. Heinz_, Jul 24 2018
%t A317223 b[_] = 0;
%t A317223 a[n_] := a[n] = Module[{t}, t = If[n<2, n, b[a[b[a[n-1]]]]]; b[t]++; t];
%t A317223 a /@ Range[0, 200] (* _Jean-François Alcover_, Nov 09 2020, after _Alois P. Heinz_ *)
%Y A317223 Cf. A316774, A317015, A317127.
%K A317223 nonn
%O A317223 0,4
%A A317223 _Altug Alkan_, Jul 24 2018