%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
