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.

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

“…One remarkable example for the V -recurrence is that the initial conditions 3, 1, 4, 4 generates a sequence that terminates after 474767 terms [5]. Similarly, the recurrence B A (n) = B A (n−B A (n−1))+B A (n−B A (n−2))+B A (n−B A (n−3)) with the initial conditions 1, 1, 1, 4, 3 dies [1] when B A (509871) = 519293. More surprisingly, Isgur notes that…”