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In this Numberphile video (from 3:36 to 7:41), Neil Sloane explains an amazing sequence: It is the lexicographically first among the sequences of positive integers without triple in arithmetic ...

Consider the following variant of the Collatz function: $f:\mathbb N\rightarrow\mathbb N$ is defined by \begin{equation} f(n):=\begin{cases} n/2 & \text{if $n$ is even}\\ 5n+1 & \...