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 A194066 #12 Dec 26 2023 10:23:48
%S A194066 1,1,2,1,2,1,2,3,1,2,3,4,1,2,3,4,1,2,3,4,5,1,2,3,4,5,6,1,2,3,4,5,6,1,
%T A194066 2,3,4,5,6,7,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,9,1,2,3,
%U A194066 4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,11,1
%N A194066 Natural fractal sequence of A087483.
%C A194066 See A194029 for definitions of natural fractal sequence and natural interspersion.
%t A194066 z = 70;
%t A194066 c[k_] := 1 + Floor[(1/3) k^2];
%t A194066 c = Table[c[k], {k, 1, z}] (* A087483 *)
%t A194066 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194066 f = Table[f[n], {n, 1, 300}] (* A194066 *)
%t A194066 r[n_] := Flatten[Position[f, n]]
%t A194066 t[n_, k_] := r[n][[k]]
%t A194066 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194066 p = Flatten[Table[t[k, n - k + 1], {n, 1, 14}, {k, 1, n}]] (* A194067 *)
%t A194066 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194068 *)
%Y A194066 Cf. A194029, A194067, A087483.
%K A194066 nonn
%O A194066 1,3
%A A194066 _Clark Kimberling_, Aug 14 2011