A194107 Natural fractal sequence of A194106.

1, 2, 3, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..89.

Mathematica

z = 40; g = Sqrt[3];
c[k_] := Sum[Floor[j*g], {j, 1, k}];
c = Table[c[k], {k, 1, z}]  (* A194106 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 800}]  (* A194107 *)
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}]]  (* A194108 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194109 *)

Crossrefs

Cf. A194029, A194106, A194108.

Sequence in context: A359264 A274641 A003315 * A071797 A338027 A025481

Adjacent sequences: A194104 A194105 A194106 * A194108 A194109 A194110

Keyword

nonn

Author

Clark Kimberling, Aug 15 2011

Status

approved