Collisions of digit sums in bases 2 and 3

2021/05/24 by Lukas Spiegelhofer, Spiegelhofer, Lukas
Computer Science · Mathematics · #11B50 #60F10 #Advanced Mathematical Identities #Benford’s Law and Fraud Detection #FOS: Mathematics #Number Theory (math.NT) #Primary: 11A63 #Secondary: 11B25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2105.11173

openalex publication_date 2021/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a folklore conjecture concerning the sum-of-digits functions in bases two and three: there are infinitely many positive integers n such that the sum of the binary digits of n equals the sum of the ternary digits of n.

Related

• The joint distribution of binary and ternary digits sums
• Binary-ternary collisions and the last significant digit of n! in base 12
• Sums of the digits in bases 2 and 3
• Settling some sum suppositions
• Somme des chiffres et changement de base