Question 157
Let $s_{1} = 2^{2010}$. For $n \gt 2$, define
$$
s_{n+1} = \begin{cases}
\log_{\sqrt{2}} s_{n}, & s_{n} \gt 0 \\
0, & s_{n} \leq 0
\end{cases}
$$
Find the smallest $n$ such that $s_{n} \in [4,6]$.
$$
s_{n+1} = \begin{cases}
\log_{\sqrt{2}} s_{n}, & s_{n} \gt 0 \\
0, & s_{n} \leq 0
\end{cases}
$$
Find the smallest $n$ such that $s_{n} \in [4,6]$.