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%I #5 Mar 30 2012 18:57:39
%S 1,2,3,1,2,3,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,
%T 8,9,1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,4,5,
%U 6,7,8,9,10,11,12,13,14,15,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
%N Natural fractal sequence of A194073.
%C See A194029 for definitions of natural fractal sequence and natural interspersion.
%t z = 70;
%t c[k_] := 1 + Floor[(3/4) k^2];
%t c = Table[c[k], {k, 1, z}] (* A194073 *)
%t f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t f = Table[f[n], {n, 1, 300}] (* A194074 *)
%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}]] (* A194075 *)
%t q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194076 *)
%Y Cf. A194073, A194075.
%K nonn
%O 1,2
%A _Clark Kimberling_, Aug 14 2011