Find the smallest term of the sequence $a_1, a_2, a_3, \ldots$ defined by $a_1=2014^{2015^{2016}}$ and $$ a_{n+1}= \begin{cases} \frac{a_n}{2} & \text{ if } a_n \text{ is even} \\ a_n + 7 & \text{ if } a_n \text{ is odd} \\ \end{cases} $$
Source: 2015 Peru Cono Sur TST P5
Tags: number theory
Find the smallest term of the sequence $a_1, a_2, a_3, \ldots$ defined by $a_1=2014^{2015^{2016}}$ and $$ a_{n+1}= \begin{cases} \frac{a_n}{2} & \text{ if } a_n \text{ is even} \\ a_n + 7 & \text{ if } a_n \text{ is odd} \\ \end{cases} $$