A194055 Natural fractal sequence of A000071 (Fibonacci numbers minus 1).

1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 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, 16, 17, 18, 19, 20, 21, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..82.

Mathematica

z = 50;
c[k_] := -1 + Fibonacci[k + 2]
c = Table[c[k], {k, 1, z}] (* A000071, F(n+2)-1 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}]   (* A194055 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 11}, {k, 1, n}]] (* A194056 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194057 *)

Crossrefs

Cf. A194029, A000071, A194056, A194057.

Sequence in context: A364604 A037125 A194029 * A162192 A329795 A329794

Adjacent sequences: A194052 A194053 A194054 * A194056 A194057 A194058

Keyword

nonn

Author

Clark Kimberling, Aug 13 2011

Status

approved