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The usual Collatz map is $C:n \mapsto n/2$ if $n$ even, $(3n+1)/2$ if $n$ odd. Let $f^{\circ (r+1)}:=f \circ f^{\circ r}$. We suspect that for every fixed $n>0$, the sequence $C^{\circ r}(n)$ ...

This post makes a focus on a very specific part of that long post. Consider the following map: $$f: n \mapsto \left\{ \begin{array}{ll} \left \lfloor{n/\sqrt{2}} \right \rfloor & \...

This post comes from the suggestion of Joel Moreira in a comment on An alternative to continued fraction and applications (itself inspired by the Numberphile video 2.920050977316 and Fridman, ...

@JosephO'Rourke asked a question about a Collatz like function related to primes: $f(n) = \begin{cases} n^2 & \text{if} \;n \;\text{is prime} \\ \lfloor n/2 \rfloor & \text{if} \;n \;\text{...