Multiplicative subsemigroups of the positive integers closed with respect to the number of digits

Abstract

In this paper we present an alternative approach to a problem dealt with by Rosales et al. In particular, once a base $b$ for the representation of the integers is fixed, we describe a procedure for constructing the smallest multiplicative subsemigroup of the positive integers closed with respect to the number of digits which contains a set of positive integers.

5 pages; exposition improved; minor fixes