A194917 Fractalization of (n-[nr-n]), where [ ]=floor and r=(1+sqrt(5))/2 (the golden ratio).

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

Offset

1,2

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (n-[nr-n]) is A189663.

Links

Table of n, a(n) for n=1..94.

Mathematica

r = GoldenRatio; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A189663 *)
g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
f[20] (*  A194917 *)
row[n_] := Position[f[30], n];
u = TableForm[Table[row[n], {n, 1, 5}]]
v[n_, k_] := Part[row[n], k];
w = Flatten[ Table[v[k, n - k + 1], {n, 1, 13},
{k, 1, n}]] (* A194918 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194919 *)

Crossrefs

Cf. A194959, A189663, A194918, A194919.

Sequence in context: A195073 A194987 A383847 * A194914 A195076 A163491

Adjacent sequences: A194914 A194915 A194916 * A194918 A194919 A194920

Keyword

nonn

Author

Clark Kimberling, Sep 08 2011

Status

approved