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