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

Altug Alkan; Nathan Fox; Orhan Ozgur Aybar; Zehra Akdeniz

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On Some Solutions to Hofstadter's V-Recurrence

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arxiv 2002.03396 v1 pith:S7R3OXLO submitted 2020-02-09 math.DS nlin.CD

On Some Solutions to Hofstadter's V-Recurrence

Altug Alkan , Nathan Fox , Orhan Ozgur Aybar , Zehra Akdeniz This is my paper

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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, $H(n)= H(n-H(n-2)) + H(n-H(n-3))$.

On Some Solutions to Hofstadter's V-Recurrence

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