Persistence of a number assumed. The single-digit final state reached in the process of calculating an integer's additive persistence is its digital root. Put another way, a number's additive persistence counts how many times we must sum its digits to arrive at its digital root. The additive persistence of 2718 is 2: first we find that 2 + 7 + 1 + 8 = 18, and then that 1 + 8 = 9. The multiplicative persistence of 39 is 3, because it takes three steps to reduce 39 to a single digit: 39 → 27 → 14 → 4. Also, 39 is the smallest
Happy number of both 1 and -1 are 1, and 1 + 1 is 2, which is the only balanced ternary cycle. For every pair of digits 1 or -1, their sum is 0 and the sum of their squares is 2 and if there are an even number of 1, -1 sets, the number divisible by 2 and sad and if odd, it is happy. In this case, the result always end in a one-digit cycle of 0, 1 or 2, repeated infinitely. In unbalanced ternary, the digits square to 1 and 4, and in this case there are 5 loops: