A function $f$ defined on integers such that $f (n) =n + 3$ if $n$ is odd $f (n) = \frac{n}{2}$ if $n$ is even If $k$ is an odd integer, determine the values for which $f (f (f (k))) = k$.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 Shortlist F1 day1 (F= functions)
Tags: algebra, function