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%I #5 Mar 30 2012 18:57:39
%S 1,2,3,1,2,3,4,1,2,3,4,5,6,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,9,1,2,3,4,
%T 5,6,7,8,9,10,11,1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,4,5,6,7,8,9,10,11,
%U 12,13,14,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8
%N Natural fractal sequence of A054347.
%C See A194029 for definitions of natural fractal sequence and natural interspersion.
%t z = 40; g = GoldenRatio
%t c[k_] := Sum[Floor[j*g], {j, 1, k}];
%t c = Table[c[k], {k, 1, z}] (* A054347 *)
%t f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t f = Table[f[n], {n, 1, 800}] (* A194053 *)
%t r[n_] := Flatten[Position[f, n]]
%t t[n_, k_] := r[n][[k]]
%t TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
%t p = Flatten[Table[t[k, n - k + 1], {n, 1, 16}, {k, 1, n}]] (* A194054 *)
%t q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194058 *)
%Y Cf. A194029.
%K nonn
%O 1,2
%A _Clark Kimberling_, Aug 15 2011
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