Abstract
In this paper, we introduce and study the iterates of the following family of functions φ k defined on natural numbers which exhibits nice properties. φ k ( x ) = { x + k , if x is prime ; largest prime divisor of x , if x is composite ; In particular, we study the periodic behavior of the trajectories of these iterated functions. In some cases, we provide proofs of these properties and in some other cases we pose some open problems based on numerical evidences supported by heuristic arguments.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have