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Let $C: \mathbb{N} \rightarrow \mathbb{N}$ be your typical collatz map (i.e. $3N+1$ for odd N, $N/2$ for even N). My question is about $f(N) =
min_{j≥1} \{|N-C^{(j)}(N)|\}$. Now, assuming Collatz Conjecture, the only solution to $f(N) = 0$ is $N \in \{1, 2, 4\}$ (because $f(N) = 0$ if and only if...
