SETS OF POSITIVE INTEGERS CLOSED UNDER PRODUCT AND THE NUMBER OF DECIMAL DIGITS

Abstract

A digital semigroup D is a subsemigroup of (N,+ ) such that if d 2 D then fx 2 Nnf0g j ℓ(x) = ℓ(d)g D with ℓ(n) the number of digits of n written in decimal expansion. In this note, we compute the smallest digital semigroup containing a set of positive integers. For this, we establish a connection between the digital semigroups and a class of numerical semigroups called LD-semigroups