On Periodic Points of the Order of Appearance in the Fibonacci Sequence

Abstract

Let (F-n)(n >= 0) be the Fibonacci sequence. The order of appearance z(n) of an integer n >= 1 is defined by z (n) = min{k >= 1 : n vertical bar F-k}. Marques, and Somer and Krizek proved that all fixed points of the function z (n) have the form n = 5(k) or 12 . 5(k). In this paper, we shall prove that z(n) does not have any k-periodic points, for k >= 2.