Some problems related to the growth of z(n)

dc.contributor.author	Trojovský, Pavel
dc.date.accessioned	2025-12-05T09:04:45Z
dc.date.available	2025-12-05T09:04:45Z
dc.date.issued	2020
dc.description.abstract	Let (Fn)n >= 0 be the Fibonacci sequence. The order of appearance z(n) of a positive integer n is defined as z(n):=min{k >= 1:n divide Fk}. In 2013, Marques proved that lim infn ->infinity z(n)/n=0. Let epsilon be a positive real number. In this paper, in particular, we generalized this Marques' result by proving that almost all positive integers satisfy z(n)/n < epsilon.	eng
dc.format	p. "Article Number: 270"
dc.identifier.doi	10.1186/s13662-020-02735-5
dc.identifier.issn	1687-1847
dc.identifier.obd	43876480
dc.identifier.scopus	2-s2.0-85086005324
dc.identifier.uri	http://hdl.handle.net/20.500.12603/1025
dc.identifier.wos	000540587200005
dc.language.iso	eng
dc.peerreviewed	yes
dc.publicationstatus	postprint
dc.publisher	Springer
dc.relation.ispartof	Advances in difference equations, volume 2020, issue: 1	eng
dc.relation.publisherversion	https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-020-02735-5
dc.rights.access	Open Access
dc.rights.license	CC BY
dc.source.url	https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-020-02735-5
dc.subject	Asymptotic	eng
dc.subject	Arithmetic functions	eng
dc.subject	Fibonacci sequence	eng
dc.subject	Order of appearance	eng
dc.subject	Natural density.	eng
dc.title	Some problems related to the growth of z(n)	eng
dc.type	article

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