On integer numbers with locally smallest order of appearance in the Fibonacci sequence
Summary: Let \(F_n\) be the be the \(n\)th 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 \(F_n\). For instance, for all \(n=F_m \geq 5\), 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.
scientific article; zbMATH DE number 5900721