Is the Syracuse falling time bounded by 12?

Shalom Eliahou, Jean Fromentin, Rénald Simonetto

Let $T:\mathbb{N}\to \mathbb{N}$ denote the $3x+1$ function, where $T(n)=n/2$ if $n$ is even, $T(n)=(3n+1)/2$ if $n$ is odd. As an accelerated version of $T$, we define a j…