A160136 Lodumo_9 of Fibonacci numbers.

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

Offset: 0

Author

Philippe Deléham, May 02 2009

Keywords

• easy
• nonn

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
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Crossrefs

Cf. A000045, A007887.

Programs

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 *)

Formula

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

a(n) = 2*a(n-24) - a(n-48) for n >= 48. - Philippe Deléham, Mar 09 2023

a(n) = a(n-12) + a(n-24) - a(n-36) for n >= 36. - Ray Chandler, Sep 10 2023

Extensions

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