Hi everyone. A few years ago i asked this question: https://math.stackexchange.com/questions/3464491/is-this-contrived-sequence-eventually-periodic and I want to return to investigate this question. In short, we start with a tape full of zeroes, fix a number n and then look at the number $t_0$ in the 0th cell, then look at the number $t_1$ in the $t_0$th cell, and so on, and then increase the number in $t_{n-1}$th sell by $1$. Then do it again and again. My goal is to describe the possible evolutions of the tape depending on the number $n$.