A162398 a(n) = the largest Fibonacci number that when represented in binary is a substring in the binary representation of n.

1, 2, 3, 2, 5, 3, 3, 8, 2, 5, 5, 3, 13, 3, 3, 8, 8, 2, 3, 5, 21, 5, 5, 8, 3, 13, 13, 3, 13, 3, 3, 8, 8, 34, 8, 2, 5, 3, 3, 8, 5, 21, 21, 5, 13, 5, 5, 8, 8, 3, 3, 13, 21, 13, 55, 8, 3, 13, 13, 3, 13, 3, 3, 8, 8, 8, 8, 34, 34, 8, 8, 8, 2, 5, 5, 3, 13, 3, 3, 8, 8, 5, 5, 21, 21, 21, 21, 8, 89, 13, 13, 5, 13, 5, 5, 8, 8, 34, 8, 3