A193042 Natural fractal sequence of A194126.

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

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 A355008

Adjacent sequences: A193039 A193040 A193041 * A193043 A193044 A193045

Keyword

nonn

Author

Clark Kimberling, Aug 15 2011

Status

approved