On a conjecture about generalized Q-recurrence

Abstract

Chaotic meta-Fibonacci sequences which are generated by intriguing examples of nonlinear recurrences still keep their mystery although substantial progress has been made in terms of well-behaved solutions of nested recurrences. In this study, a recent generalization of Hofstadter's famous Q-sequence is studied beyond the known methods of generational approaches in order to propose a generalized conjecture regarding the existence of infinitely many different solutions for all corresponding recurrences of this generalization.