Minimal Niven numbers

TL;DR

This paper investigates the properties and bounds of minimal Niven numbers, which are the smallest multiples of k with digit sum k in a given base q, including their asymptotic behavior and minimality conditions.

Contribution

It provides new bounds, asymptotic analysis, and a characterization of minimal Niven numbers, advancing understanding of their properties across different bases.

Findings

Derived bounds for a(k,q)

Analyzed asymptotic behavior of a(k,q)

Characterized minimality conditions for Niven numbers

Abstract

Define a(k,q) to be the smallest positive multiple of k such that the sum of its digits in base q is equal to k. The asymptotic behavior, lower and upper bound estimates of a(k,q) are investigated. A characterization of the minimality condition is also considered.