8-Cycle
Take any number n (a positive integer), square its digits, and add them up. What you get is a new number which we will call T(n). T is a transformation that changes one number into another. Our objective here is to understand what happens when we apply that transformation again and again,
For example, Suppose we start with 2021. Then apply T again and again:
2021 —> 9 —> 81 —> 65 —> 61 —> 37 —> 58 —> 89 —> 145 …
and we keep right on going. What eventually happens? What happens for other starting numbers?
