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Let 

\[f(n) = \begin{cases} 3n + 1 & \text{if }n\text{ is odd} \\ \dfrac{n}{2} & \text{if }n\text{ is even} \end{cases}.\]

 

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?

 
 Jan 12, 2021

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