Question 123
An increasing sequence of positive integers $\{a_n\}$ and a positive integer $k$ are given. For each positive integer $n$ the following conditions hold: the number $a_n$ is divisible either by $1005$ or by $1006$, $a_n$ is not divisible by $97$, and $a_{n+1} - a_n \le k$. Find the least possible value of $k$. (A. Golovanov)