A194074 Natural fractal sequence of A194073.

1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 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, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..90.

Mathematica

z = 70;
c[k_] := 1 + Floor[(3/4) k^2];
c = Table[c[k], {k, 1, z}]  (* A194073 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}]   (* A194074 *)
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, 14}, {k, 1, n}]] (* A194075 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]]  (* A194076 *)

Crossrefs

Cf. A194073, A194075.

Sequence in context: A343638 A293207 A106590 * A175469 A239526 A371822

Adjacent sequences: A194071 A194072 A194073 * A194075 A194076 A194077

Keyword

nonn

Author

Clark Kimberling, Aug 14 2011

Status

approved