Consider the sequence given by $a_0 = 3$ and such that for $i \ge 1$, we have $ai = 2^{a_{i-1}} + 1$. Let $m$ be the smallest integer such that $a^3_3$ divides $a_m$. Let $m'$ the smallest integer such that $a^3_m$ divides $a_{m'}$ . Find the value of $m'$.

Let's think step by step and output the final answer within \boxed{}.
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