+67 \(Let f(n) = \begin{cases} n^2+1 & \text{if }n\text{ is odd} \\ \dfrac{n}{2} & \text{if }n\text{ is even} \end{cases}.\)
\(For\:how \:many \:integers \:n \:from \:1 \:to \:100, inclusive, does \:f ( f (\dotsb f (n) \dotsb )) = 1 \:for\: some \:number\: of \:applications \:of \:f? \)
