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

2012/03/20 by Anunay Kulshrestha, Kulshrestha, Anunay
Computer Science · Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Mathematics and Applications #cs.DM

paper · pdf · doi:10.48550/arxiv.1203.4547

openalex publication_date 2012/03/20 · arxiv created 2012/04/29 · arxiv updated 2012/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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