This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A232564 #4 Nov 27 2013 13:30:07
%S A232564 1,2,4,3,6,11,21,5,9,17,33,8,15,29,56,7,13,25,48,12,23,44,85,22,42,81,
%T A232564 156,41,79,152,293,10,19,37,71,18,35,67,129,34,65,125,241,64,123,237,
%U A232564 457,16,31,60,115,30,58,111,214,57,109,210,405,108,208,401
%N A232564 Inverse permutation of the sequence of positive integers at A232563.
%H A232564 Clark Kimberling, <a href="/A232564/b232564.txt">Table of n, a(n) for n = 1..1000</a>
%t A232564 z = 8; g[1] = {1}; g[2] = {2, 4}; g[n_] := Riffle[g[n - 1] + 1, 4 g[n - 1]]; j[2] = Join[g[1], g[2]]; j[n_] := Join[j[n - 1], g[n]]; g1[n_] := DeleteDuplicates[DeleteCases[g[n], Alternatives @@ j[n - 1]]]; g1[1] = g[1]; g1[2] = g[2]; t = Flatten[Table[g1[n], {n, 1, z}]] (* A232563 *)
%t A232564 Table[Length[g1[n]], {n, 1, z}] (* A001631 *)
%t A232564 t1 = Flatten[Table[Position[t, n], {n, 1, 200}]] (* A232564 *)
%Y A232564 Cf. A232559, A232563.
%K A232564 nonn,easy
%O A232564 1,2
%A A232564 _Clark Kimberling_, Nov 26 2013