|
| |
|
|
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.
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, 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.
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).
|
|
|
FORMULA
|
a(n) = a(n-12) + a(n-24) - a(n-36) for n >= 36. - Ray Chandler, Sep 10 2023
|
|
|
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
|
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
