# 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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