Permutation--invariant Niven numbers

TL;DR

This paper defines a new class of Niven numbers that remain Niven numbers under any digit permutation, proves their infinite existence, and provides a method to find them.

Contribution

It introduces permutation-invariant Niven numbers, establishing their infinite occurrence and presenting an exhaustive search approach for identification.

Findings

Infinitely many permutation-invariant Niven numbers exist.

Their magnitude is unbounded.

An exhaustive search method for these numbers is developed.

Abstract

This paper introduces permutation-invariant Niven numbers--a novel class of Niven numbers where all digit permutations (with leading zeros automatically ignored) must retain the Niven property. We demonstrate that there exist infinitely many such numbers and that their magnitude is unbounded. Furthermore, we present an exhaustive search method for identifying permutation--invariant Niven numbers.