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Smith multiples of a class of primes with small digital sum. (English) Zbl 1401.11013
Summary: 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.
##### MSC:
 11A63 Radix representation; digital problems 11A41 Primes
##### Keywords:
Smith numbers; sum of digits
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