A Fibonacci theorem for Collatz trajectories via modular graph structure

Manuel-Alejandro Reyes Jiménez

Let $T(n)=n/2$ if $n$ is even and $T(n)=(3n+1)/2$ if $n$ is odd. We prove that for each $m\ge 1$, exactly $F(m+1)$ odd integers $n$ in $\{1,\dots ,2^m\}$ have the property that none…