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 finding large Osiris numbers in a particular base. For example, to test by brute force whether permutated six-digit samples of "n" = 332,639,667,360 are equal to "n" would involve summing 665,280 numbers, where 665,280 = 12 x 11 x 10 x 9 x 8 x 7 = 12! / 6!. However, because each digit of "n" occurs 55440 times in each of the six possible positions in the samples, the test is reduced to this: Digit-reassembly number Digit-reassembly numbers, or Osiris numbers, are numbers that are equal to the sum of permutations of sub-samples of their own digits (compare the