Question 97
Let $c$ be a non-negative integer. Find all sequences of positive integers $\{a_n\}_{n \ge 1}$ such that for any positive integer $n$, the following condition holds:
There are exactly $a_n$ positive integers $i$ satisfying $a_i \le a_{n+1} + c$.
There are exactly $a_n$ positive integers $i$ satisfying $a_i \le a_{n+1} + c$.