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A194917 Fractalization of (n-[nr-n]), 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 (list; graph; refs; listen; history; text; internal format)
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: A194983 A195073 A194987 * A194914 A195076 A163491

Adjacent sequences:  A194914 A194915 A194916 * A194918 A194919 A194920

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 08 2011

STATUS

approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)