On the Hamming Distance between base-n representations of whole numbers

Abstract

We first introduce the Hamming distance between two strings. Then, we apply this concept to the representations of whole numbers in base n for all positive integers n > 2. We claim that a simple formula exists for the sum of all Hamming distances between pairs of consec- utive integers from 1 to m, which we will derive. We also state and prove other interesting results concerning the aforementioned topic.