given some positive integer $x_0$ as starting value. The sequence should terminate when

$x_n=1.$ Nobody has yet been able to prove that the sequence will always terminate in a

finite number of steps, for all positive integers $x_0,$ although this has now been verified $($by

brute force$)$ for all starting integers through $52^{60}($which is a very big number$).$

Run your program with $x_0=m$ for each of the integers $m$ from $1$ through $300.$ Draw a graph

with the values of $x_0=m$ on the $x-$axis, and the number of steps the sequence takes to

terminate when starting from $x_0=m$ on the $y-$axis. For that $x_0$ with the largest number of

steps, draw a graph with the values of $k$ on the $x-$axis and the values of $x_k$ on the $y-$axis.