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
Keith number Keith number In recreational mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a number in the following integer sequence: Keith numbers were introduced by Mike Keith in 1987. They are computationally very challenging to find, with only about 100 known. To determine whether an "n"-digit number "N" is a Keith number, create a Fibonacci-like sequence that starts with the "n" decimal digits of "N", putting the most significant digit first. Then continue the sequence, where each subsequent term is the sum of the previous "n" terms. By definition, "N" is a Keith number if "N"