sentences:  This is because all natural numbers of base formula_1 with formula_23 digits satisfy formula_35.However, when formula_36, then formula_37 for formula_38, so any formula_2 will satisfy formula_40 until formula_41.There are a finite number of natural numbers less than formula_42, so the number is guaranteed to reach a periodic point or a fixed point less than formula_43, making it a preperiodic point.