Crazy Collapsible Collatz

Number Theory Level pending

Consider the Collatz function defined on the positive integers:

\[ f(n) = \begin{cases} \frac {n}{2} & n \mbox{ even} \\ 3n+1 & n \mbox{ odd} \\ \end{cases} \]

Find the smallest value of \(n\) such that \( f^{(7)} (n) = 5 \).

Details and assumptions

\( f^{(7)} (n) \) means the function \(f\) applied 7 times. I.e. \( f^{(7)} (n) = f(f(f(f(f(f(f(n)))))))\).

Note that the function is only defined on the positive integers. Hence, your answer must be a positive integer.


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