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
Normal number Normal number In mathematics, a normal number is a real number whose infinite sequence of digits in every positive integer base b is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b, also all possible b pairs of digits are equally likely with density b, all b triplets of digits equally likely with density b, etc. Intuitively this means that no digit, or (finite) combination of digits, occurs more frequently than any other, and this is true whether the number is written in base 10, binary, or any other base. A