On Some Solutions to Hofstadter's V-Recurrence

2020/02/09 by Altug Alkan, Nathan Fox, Alkan, Altug +5
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2002.03396

openalex publication_date 2020/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this study, we explore the properties of certain solutions of Hofstadter's famous V-recurrence, defined by the nested recurrence relation V(n)=V(n-V(n-1))+V(n-V(n-4)). First, we discover the nature behind a finite chaotic meta-Fibonacci sequence in terms of mortality in the V-recurrence. Then, we construct a new kind of quasi-periodic solution which suggests a connection with another Hofstadter-Huber recursion, H(n)= H(n-H(n-2)) + H(n-H(n-3)).

Citations

• The transmittivity of a Bose–Einstein condensate on a lattice: interference from period doubling and the effect of disorder

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