Question 161
Call a number feared if it contains the digits $13$ as a contiguous substring and fearless otherwise. (For example, $132$ is feared, while $123$ is fearless.) Compute the smallest positive integer $n$ such that there exists a positive integer $a\lt 100$ such that $n$ and $n+10a$ are fearless while $n+a, n+2a, \ldots, n+9a$ are all feared.