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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 \(f\)?

 Oct 9, 2019

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