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
Automorphic number 6. One of them has the form: and the other has the form: The sum of the two numbers is 10 + 1. The smaller of these two numbers may be less than 10; for example with "k" = 4 the two numbers are 9376 and 625. In this case there is only one "k" digit automorphic number; the smaller number could only form a "k"-digit automorphic number if a leading 0 were added to its digits. The following digit sequence can be used to find the two "k"-digit automorphic numbers, where "k" ≤ 1000. One automorphic number is found