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
Digit-reassembly number the permutated sums: If zero is treated as a full digit in all positions, then 207 in base ten is a maximal Osiris number, being equal to the sum of all possible distinct numbers formed from permutated sub-samples of its digits: In other bases, maximal Osiris numbers exist that do not contain zeros. For example: Using the same terminology, 132, 264 and 396 are minimal Osiris numbers, being equal to the sums of all numbers formed from permutated samples of only two of their digits. 35964 is also minimal, being the sum of samples of three digits, but 34658 is