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arXiv · 2002.03396

On Some Solutions to Hofstadter's $V$-Recurrence

Altug Alkan·Nathan Fox·Orhan Ozgur Aybar·Zehra Akdeniz
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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, $H(n)= H(n-H(n-2)) + H(n-H(n-3))$.

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Altug Alkan, Nathan Fox, Orhan Ozgur Aybar, Zehra Akdeniz. 2020-02-09. On Some Solutions to Hofstadter's $V$-Recurrence. https://arxiv.org/abs/2002.03396

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