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
Elementary arithmetic number. Find the sum of these two digits: write this sum under the line and in the ones-column. If the sum has two digits, then write down only the ones-digit of the sum. Write the "carry digit" above the top digit of the next column: in this case the next column is the tens-column, so write a 1 above the tens-digit of the first number. If both first and second number each have only one digit then their sum is given in the addition table, and the addition algorithm is unnecessary. Then comes the tens-column. The tens-column might contain two