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Successive remainders when computing the euclidean algorithm for (n,m) where m is any positive integer having no common factor with n, gives a list ending with a sublist of Fibonacci sequence. Find m such that this sublist has the greatest length, and define a(n) as this length.

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0, 0, 1, 2, 1, 3, 1, 2, 4, 2, 1, 3, 2, 5, 3, 2, 2, 3, 4, 3, 3, 6, 2, 4, 2, 3, 3, 3, 4, 5, 3, 4, 3, 4, 7, 3, 3, 5, 4, 3, 2, 4, 2, 4, 4, 5, 3, 6, 4, 4, 5, 4, 3, 5, 3, 8, 3, 4, 4, 4, 6, 5, 3, 4, 4, 3, 5, 4, 4, 5, 4, 5, 3, 6, 4, 4, 7, 5, 4, 5, 4, 6, 5, 4, 3, 5, 6, 4, 4, 9, 3, 4, 5, 5, 4, 5, 4, 7, 5, 6, 4, 5, 3, 5, 4 (list; graph; listen)

	OFFSET	`0,4`
	EXAMPLE	`a(5) = 3 because computing euclidean algorithm for (5,8) gives 3, 2, 1 as successive remainders, all three belonging to Fibonacci sequence.`
	CROSSREFS	`Sequence in context: A089384 A057059 A027750 this_sequence A130517 A056951 A130212` `Adjacent sequences: A087292 A087293 A087294 this_sequence A087296 A087297 A087298`
	KEYWORD	`easy,nonn`
	AUTHOR	`Thomas Baruchel (baruchel(AT)users.sourceforge.net), Oct 19 2003`

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Last modified July 23 17:35 EDT 2008. Contains 142285 sequences.

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