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, 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