A construction of minimal asymptotic bases

Abstract

Jia and Nathanson [2] give a simple and explicit construction of minimal asymptotic bases of orderh for everyh≥2. They constructed minimal asymptotic bases from partition of N by means of powers of 2. In this paper, we extend the results of that paper to asymptotic bases constructed from partitions of N by means ofg-adic representations forg≥2. Corollary 3 shows that given partition N=W ₀⌣W ₁⌣...⌣W _h−1 such that eachW _i contains infinitely many pairs of consecutive integers we can construct a minimal asymptotic bases of orderh in infinitely many way.