

A194917


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


3



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
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OFFSET

1,2


COMMENTS

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. The sequence (n[nrn]) 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: A194983 A195073 A194987 * A194914 A195076 A163491
Adjacent sequences: A194914 A194915 A194916 * A194918 A194919 A194920


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 08 2011


STATUS

approved



