Fixed Points of the Josephus Function via Fractional Base Expansions

2025/06/30 by Bello-Cruz, Yunier, Quintero-Contreras, Roy
#11B37 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2507.00317

Abstract

In this paper, we investigated some interesting properties of the fixed points of the Josephus function J₃. First, we establish a connection between this sequence and the Chinese Remainder Theorem. Next, we observed a clear numerical pattern in the fixed points sequence when the terms are written in base 3/2 using modular arithmetic, which allows us to develop a recursive procedure to determine the digits of their base 3/2 expansions.

Citations

• On the Recurrence Formula for Fixed Points of the Josephus Function
• Analytical Study and Efficient Evaluation of the Josephus Function
• A number system with base -\frac32

Related

• On the Recurrence Formula for Fixed Points of the Josephus Function
• Analytical Study and Efficient Evaluation of the Josephus Function
• On a sequence related to the Josephus problem
• Maximum Nim and Josephus Problem algorithm
• New Congruences and Finite Difference Equations for Generalized Factorial Functions