2002 AIME I Problem 8

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.