A161553 - OEIS

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A161553

Table which contains in row n the fundamental Pisano period of the Fibonacci sequence (mod n).

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; internal format)

	OFFSET	`1,8`
	COMMENTS	`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.` `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}.`
	CROSSREFS	`Cf. A000045, A001175.` `Sequence in context: A155100 A076880 A082115 * A099751 A159937 A058728` `Adjacent sequences: A161550 A161551 A161552 * 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 February 13 11:49 EST 2012. Contains 205468 sequences.