On integer numbers with locally smallest order of appearance in the Fibonacci sequence
type: Item
instance of: scholarly article
title: On integer numbers with locally smallest order of appearance in the Fibonacci sequence
zbMATH Open document ID: 1314.11007
DOI: 10.1155/2011/407643
author: Diego Marques
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-05-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 5900721
zbMATH Keywords: Fibonacci sequence
zbMATH Keywords: Fibonacci entry point
zbMATH Keywords: Binet's formula
Wikidata QID: Q58687777
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/407643
OpenAlex ID: W2067820165
cites work: Fibonacci and Lucas numbers with applications. Volume I
cites work: Existence of primitive divisors of Lucas and Lehmer numbers (with an appendix by M. Mignotte)
DBLP publication ID: journals/ijmmsc/Marques11
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description: scientific article; zbMATH DE number 5900721