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A161553 Table which contains in row n the fundamental Pisano period of the Fibonacci sequence (mod n). +0
1
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; listen)
OFFSET

1,8

COMMENT

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

LINKS

Eric Weisstein's World of Mathematics, Pisano Period.

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

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}.

CROSSREFS

Cf. A000045, A001175.

Sequence in context: A155100 A076880 A082115 this_sequence A099751 A159937 A058728

Adjacent sequences: A161550 A161551 A161552 this_sequence A161554 A161555 A161556

KEYWORD

nonn,tabf

AUTHOR

Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 13 2009

EXTENSIONS

Moved into the keyword:tabf category - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 04 2009

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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