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%I A193042 #13 Mar 30 2012 18:57:38
%S A193042 1,2,3,4,5,1,2,3,4,5,6,7,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,11,
%T A193042 12,13,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,4,5,6,7,8,9,10,11,12,
%U A193042 13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17
%N A193042 Natural fractal sequence of A194126.
%C A193042 See A194029 for definitions of natural fractal sequence and natural interspersion.
%t A193042 z = 40; g = GoldenRatio;
%t A193042 c[k_] := -1 + Sum[Floor[j + j*g], {j, 1, k}];
%t A193042 c = Table[c[k], {k, 1, z}]  (* A194126 *)
%t A193042 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A193042 f = Table[f[n], {n, 1, 800}]  (* A193042 *)
%t A193042 r[n_] := Flatten[Position[f, n]]
%t A193042 t[n_, k_] := r[n][[k]]
%t A193042 TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
%t A193042 p = Flatten[Table[t[k, n - k + 1], {n, 1, 16}, {k, 1, n}]]  (* A194100 *)
%t A193042 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194101 *)
%Y A193042 Cf. A194029, A194126, A194100.
%K A193042 nonn
%O A193042 1,2
%A A193042 _Clark Kimberling_, Aug 15 2011

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