Collatz sequence

For a positive integer $a_0$, define $a_{k+1}=a_k/2$ when $a_k$ is an even number, and $a_{k+1}=3a_k+1$ when $a_k$ is an odd number. Starting at $6$ gives $6,3,10,5,16,8,4,2,1$. Computing many trajectories benefits from memoization, since trajectories that reach the same value have identical continuations.