On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence

الملخص EN

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)

In this paper, we will construct infinitely many natural numbers satisfying the previous inequalities and which do not belong to the Fibonacci sequence.