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A087295 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. 0

%I

%S 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,

%T 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,

%U 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

%N 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.

%e a(5) = 3 because computing Euclidean algorithm for (5,8) gives 3, 2, 1 as successive remainders, all three belonging to Fibonacci sequence.

%K easy,nonn

%O 0,4

%A _Thomas Baruchel_, Oct 19 2003

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Last modified January 26 23:54 EST 2022. Contains 350601 sequences. (Running on oeis4.)