Smith Multiples of a Class of Primes with Small Digital Sum

Amin Witno

Abstract

Using prime numbers whose digits are zeros and ones, we demonstrate how to construct integers $m$ for which $mP$ is a Smith number for any prime $P$ with a fixed, small digital sum. Conversely, using numbers with small digital sums, we can obtain Smith multiples of a given prime whose digits are zeros and ones. Our approach relies on small digital sums in order that every multiplication process is free from carries.