On the Recurrence Formula for Fixed Points of the Josephus Function

2023/08/22 by Cruz, Yunier Bello, Quintero-Contreras, Roy · 1 citation
#11B50 #11Y55 #65Q30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.12984

Abstract

In this paper, we provide a comprehensive solution to the open problem regarding the existence of a recurrence formula for computing fixed points of the Josephus function precisely when the reduction constant is three. Incorporating this formula into recursive algorithms significantly improves addressing the Josephus problem, particularly for large inputs.

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• Fixed Points of the Josephus Function via Fractional Base Expansions

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