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A160136 Lodumo_9 of Fibonacci numbers. 1
0, 1, 10, 2, 3, 5, 8, 4, 12, 7, 19, 17, 9, 26, 35, 16, 6, 13, 28, 14, 15, 11, 44, 37, 18, 46, 55, 20, 21, 23, 53, 22, 30, 25, 64, 62, 27, 71, 80, 34, 24, 31, 73, 32, 33, 29, 89, 82, 36, 91, 100, 38, 39, 41, 98, 40, 48, 43, 109, 107, 45, 116, 125, 52, 42, 49, 118, 50, 51, 47, 134 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Permutation of nonnegative integers.

From Michael De Vlieger, Jan 21 2021: (Start)

The plot is governed by A001175(9) = 24 and is bifurcated into two trajectories that repeat a "constellation" of points we label "red" and "blue" so as to match the linked figures. We might group the terms in a(n) into two classes as to their residue r (mod 24). The red terms have n = r (mod 24) for r in {1, 2, 6, 10, 11, 13, 14, 18, 22, 23}, while the blue terms have r in {0, 3, 4, 5, 7, 8, 9, 12, 15, 16, 17, 19, 20, 21}.

There are 10 residues in the red constellation, and 14 residues in the blue constellation.

For red, we have the displacement a(n + 24) - a(n) = 45, thus the slope m_red = 15/8. For blue, we have the displacement a(n + 24) - a(n) = 18, thus the slope m_blue = 3/4.(End)

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..9999

Michael De Vlieger, Plot (n, a(n)) for 1 <= n <=144 illustrating bifurcation into two rays color coded red and blue, and the effect of the Pisano number (mod 9) = 24.

Michael De Vlieger, Plot (n, a(n)) for 1 <= n <= 24 with the 2 rays color coded red and blue, with coordinates of points labeled.

OEIS wiki, Lodumo transform

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = lod_9(A000045(n)).

MATHEMATICA

Block[{m = 9, s = Fibonacci[Range[120]]}, Nest[Append[#1, Block[{k = 1}, While[Nand[Mod[k, m] == Mod[s[[#2]], m], FreeQ[#1, k]], k++]; k]] & @@ {#, Length@ #} &, {0}, 120]] (* Michael De Vlieger, Jan 21 2021 *)

CROSSREFS

Cf. A000045, A007887.

Sequence in context: A010175 A323421 A306321 * A333478 A336954 A322467

Adjacent sequences:  A160133 A160134 A160135 * A160137 A160138 A160139

KEYWORD

easy,nonn

AUTHOR

Philippe Deléham, May 02 2009

EXTENSIONS

Replaced second 18 by 118 - R. J. Mathar, May 03 2009

STATUS

approved

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Last modified January 20 06:36 EST 2022. Contains 350467 sequences. (Running on oeis4.)