Find the smallest integer k for which the conditions
(1) \(a_1, a_2, a_3, \ldots\) is a nondecreasing sequence of positive integers
(2) \(a_n=a_{n-1}+a_{n-2}\) for all \(n>2\)
(3) \(a_9=k\)
are satisfied by more than one sequence.
(第二十届AIME1 2002 第8题)