An exploration of solutions to two related Hofstadter-Huber recurrence relations

Altug Alkan, Nathan Fox, Orhan Ozgur Aybar and Zehra Akdeniz

Chaos, Solitons & Fractals, 2020, vol. 138, issue C

Abstract: In this study, we explore the properties of certain solutions of two Hofstadter-Huber recurrence relations. The first is Hofstadter’s V-recurrence, which is defined by the nested recurrence relation V(n)=V(n−V(n−1))+V(n−V(n−4)). Plus, we introduce another meta-Fibonacci recurrence H(n)=H(n−H(n−2))+H(n−H(n−3)). First, we study a finite chaotic solution to the V-recurrence in order to analyse its generational structure. Then, we explore a new type of infinite solution to nested recurrence relations, finding solutions of this type to both the V-recurrence and the H-recurrence. Our construction relates to systems of nested recurrences that resemble Golomb’s recurrence G(n)=G(n−G(n−1))+1.

Keywords: Meta-Fibonacci; Hofstadter V-recurrence; Familes of solutions to nested recurrences (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303003

DOI: 10.1016/j.chaos.2020.109900

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