On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence
Diego Marques · International Journal of Mathematics and Mathematical Sciences · 2011
Let Fn be the nth Fibonacci number. The order of appearance z(n) of a natural number n is defined as the smallest natural number k such that n divides Fk. For instance, for all n = Fm ≥ 5, we have z(n − 1) > z(n) < z(n + 1). In this paper, we will construct infinitely many natural numbers satisfying the previous inequalities and which do not belong to the Fibonacci sequence.