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A193042 Natural fractal sequence of A194126. 2
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, 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, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194029 for definitions of natural fractal sequence and natural interspersion.

LINKS

Table of n, a(n) for n=1..85.

MATHEMATICA

z = 40; g = GoldenRatio;

c[k_] := -1 + Sum[Floor[j + j*g], {j, 1, k}];

c = Table[c[k], {k, 1, z}]  (* A194126 *)

f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]

f = Table[f[n], {n, 1, 800}]  (* A193042 *)

r[n_] := Flatten[Position[f, n]]

t[n_, k_] := r[n][[k]]

TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]

p = Flatten[Table[t[k, n - k + 1], {n, 1, 16}, {k, 1, n}]]  (* A194100 *)

q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194101 *)

CROSSREFS

Cf. A194029, A194126, A194100.

Sequence in context: A283370 A053827 A033926 * A327463 A279478 A050269

Adjacent sequences:  A193039 A193040 A193041 * A193043 A193044 A193045

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 15 2011

STATUS

approved

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)