On the Parity of the Order of Appearance in the Fibonacci Sequence

dc.rights.license	CC BY	eng
dc.contributor.author	Trojovský, Pavel	cze
dc.date.accessioned	2025-12-05T10:23:08Z
dc.date.available	2025-12-05T10:23:08Z
dc.date.issued	2021	eng
dc.identifier.issn	2227-7390	eng
dc.identifier.uri	http://hdl.handle.net/20.500.12603/1285
dc.description.abstract	Let (F-n)(n >= 0) be the Fibonacci sequence. The order of appearance function (in the Fibonacci sequence) z : Z(>= 1)-> Z(>= 1) is defined as z(n) := min{k >= 1 : F-k equivalent to 0 (mod n)}. In this paper, among other things, we prove that z(n) is an even number for almost all positive integers n (i.e., the set of such n has natural density equal to 1).	eng
dc.format	p. "Article Number:1928"	eng
dc.language.iso	eng	eng
dc.publisher	MDPI-Molecular diversity preservation international	eng
dc.relation.ispartof	Mathematics, volume 9, issue: 16	eng
dc.subject	order of appearance	eng
dc.subject	Fibonacci numbers	eng
dc.subject	parity	eng
dc.subject	natural density	eng
dc.subject	prime numbers	eng
dc.title	On the Parity of the Order of Appearance in the Fibonacci Sequence	eng
dc.type	article	eng
dc.identifier.obd	43877890	eng
dc.identifier.doi	10.3390/math9161928	eng
dc.publicationstatus	postprint	eng
dc.peerreviewed	yes	eng
dc.source.url	https://www.mdpi.com/2227-7390/9/16/1928	cze
dc.relation.publisherversion	https://www.mdpi.com/2227-7390/9/16/1928	eng
dc.rights.access	Open Access	eng