Crazy Collapsible Collatz

Number Theory Level pending

Consider the Collatz function defined on the positive integers:

f(n)={n2n even3n+1n odd f(n) = \begin{cases} \frac {n}{2} & n \mbox{ even} \\ 3n+1 & n \mbox{ odd} \\ \end{cases}

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

Details and assumptions

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