Question 28
Define the sequence $\{a\}_{n}$ of positive integers as follows. $a_{1} = m$. $a_{n + 1} = a_{n}$ plus the product of the digits of $a_{n}$. For example, if $m = 5$, we have $5, 10, 10, \ldots$. Is there an $m$ for which the sequence is unbounded?