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A161553 Table which contains in row n the fundamental Pisano period of the Fibonacci sequence (mod n). 2
0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 0, 1, 1, 2, 3, 5, 1, 6, 0, 6, 6, 5, 4, 2, 6, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 0, 8, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

The length of the n-th row (the length of the period) is A001175(n).

LINKS

Table of n, a(n) for n=1..105.

J. D. Fulton, W. L. Morris, On arithmetical functions related to the Fibonacci numbers Acta Arithm. 16 (1969) 106-110.

Wayne Peng, ABC Implies There are Infinitely Many non-Fibonacci-Wieferich Primes - An Application of ABC Conjecture over Number Fields, arXiv:1511.05645 [math.NT], 2015.

Eric Weisstein's World of Mathematics, Pisano Period.

Wikipedia, Pisano period

EXAMPLE

F(n) mod 1 {0},

F(n) mod 2 {0,1,1},

F(n) mod 3 {0,1,1,2,0,2,2,1},

F(n) mod 4 {0,1,1,2,3,1},

F(n) mod 5 {0,1,1,2,3,0,3,3,1,4,0,4,4,3,2,0,2,2,4,1},

F(n) mod 6 {0,1,1,2,3,5,2,1,3,4,1,5,0,5,5,4,3,1,4,5,3,2,5,1},

F(n) mod 7 {0,1,1,2,3,5,1,6,0,6,6,5,4,2,6,1},

F(n) mod 8 {0,1,1,2,3,5,0,5,5,2,7,1},

F(n) mod 9 {0,1,1,2,3,5,8,4,3,7,1,8,0,8,8,7,6,4,1,5,6,2,8,1},

F(n) mod 10 {0,1,1,2,3,5,8,3,1,4,5,9,4,3,7,0,7,7,4,1,5,6,1,7,8,5,3,8, 1,9,0,9,9,8,7,5,2,7,9,6,5,1,6,7,3,0,3,3,6,9,5,4,9,3,2,5,7,2,9,1}.

MATHEMATICA

per[1] = 1; per[n_] := For[k = 1, True, k++, If[Mod[Fibonacci[k], n] == 0 && Mod[Fibonacci[k + 1], n] == 1, Return[k]]];

row[n_] := Table[Mod[Fibonacci[k], n], {k, 0, per[n]-1}];

Array[row, 9] // Flatten (* Jean-Fran├žois Alcover, Oct 30 2018 *)

CROSSREFS

Cf. A000045, A001175.

Sequence in context: A155100 A076880 A082115 * A256232 A099751 A159937

Adjacent sequences:  A161550 A161551 A161552 * A161554 A161555 A161556

KEYWORD

nonn,tabf

AUTHOR

Alexander Adamchuk, Jun 13 2009

EXTENSIONS

Moved into the keyword:tabf category by R. J. Mathar, Oct 04 2009

STATUS

approved

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Last modified December 9 17:18 EST 2019. Contains 329879 sequences. (Running on oeis4.)