On integer numbers with locally smallest order of appearance in the Fibonacci sequence
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| Hlavní autor: | |
|---|---|
| Datum vydání: | 2011 |
| Médium: | Article |
| Jazyk: | eng |
| Zdroj: | Repositório Institucional da UnB |
| Download full: | http://repositorio.unb.br/handle/10482/12760 https://dx.doi.org/10.1155/2011/407643 |
Shrnutí: | 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 <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. |
| _version_ | 1871442287645425664 |
|---|---|
| author | Ferreira, Diego Marques |
| author_browse | Ferreira, Diego Marques |
| author_facet | Ferreira, Diego Marques |
| author_role | author |
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| bitstream.checksumAlgorithm.fl_str_mv | MD5 MD5 MD5 |
| bitstream.url.fl_str_mv | http://repositorio2.unb.br/jspui/bitstream/10482/12760/1/ARTIGO_OnIntegerNumbers.pdf http://repositorio2.unb.br/jspui/bitstream/10482/12760/2/license.txt http://repositorio2.unb.br/jspui/bitstream/10482/12760/3/ARTIGO_OnIntegerNumbers.pdf.txt |
| collection | Repositório Institucional da UnB |
| dc.contributor.author.fl_str_mv | Ferreira, Diego Marques |
| dc.date.accessioned.fl_str_mv | 2013-04-09T18:36:13Z |
| dc.date.available.fl_str_mv | 2013-04-09T18:36:13Z |
| dc.date.issued.fl_str_mv | 2011 |
| dc.identifier.citation.fl_str_mv | MARQUES, Diego. On integer numbers with locally smallest order of appearance in the Fibonacci sequence. International Journal of Mathematics and Mathematical Sciences, v. 2011, 2011. Disponível em: <http://www.hindawi.com/journals/ijmms/2011/407643/>. Acesso em: 22 mar. 2013. DOI: 10.1155/2011/407643. |
| dc.identifier.doi.en.fl_str_mv | https://dx.doi.org/10.1155/2011/407643 |
| dc.identifier.uri.fl_str_mv | http://repositorio.unb.br/handle/10482/12760 |
| dc.language.iso.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Hindawi Publishing Corporation |
| dc.rights.driver.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:Repositório Institucional da UnB instname:Universidade de Brasília (UnB) instacron:UNB |
| dc.subject.keyword.en.fl_str_mv | Sequências (Matemática) Equações integrais Cálculo integral |
| dc.title.en.fl_str_mv | On integer numbers with locally smallest order of appearance in the Fibonacci sequence |
| dc.type.driver.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.status.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | 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 <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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | UNB_3f8a871dcc57eaef8337972d48d65f2a |
| identifier_str_mv | MARQUES, Diego. On integer numbers with locally smallest order of appearance in the Fibonacci sequence. International Journal of Mathematics and Mathematical Sciences, v. 2011, 2011. Disponível em: <http://www.hindawi.com/journals/ijmms/2011/407643/>. Acesso em: 22 mar. 2013. DOI: 10.1155/2011/407643. |
| instacron_str | UNB |
| institution | UNB |
| instname_str | Universidade de Brasília (UnB) |
| language | eng |
| network_acronym_str | UNB |
| network_name_str | Repositório Institucional da UnB |
| oai_identifier_str | oai:repositorio.unb.br:10482/12760 |
| publishDate | 2011 |
| publishDateSort | 2011 |
| publisher.none.fl_str_mv | Hindawi Publishing Corporation |
| reponame_str | Repositório Institucional da UnB |
| repository.mail.fl_str_mv | repositorio@unb.br |
| repository.name.fl_str_mv | Repositório Institucional da UnB - Universidade de Brasília (UnB) |
| repository_id_str | |
| spelling | Ferreira, Diego Marques2013-04-09T18:36:13Z2013-04-09T18:36:13Z2011MARQUES, Diego. On integer numbers with locally smallest order of appearance in the Fibonacci sequence. International Journal of Mathematics and Mathematical Sciences, v. 2011, 2011. Disponível em: <http://www.hindawi.com/journals/ijmms/2011/407643/>. Acesso em: 22 mar. 2013. DOI: 10.1155/2011/407643.http://repositorio.unb.br/handle/10482/12760https://dx.doi.org/10.1155/2011/407643Let 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 <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.Hindawi Publishing Corporation© 2011DiegoMarques.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Fonte: http://www.hindawi.com/journals/ijmms/2011/407643/. Acesso em: 22 mar. 2013.info:eu-repo/semantics/openAccessOn integer numbers with locally smallest order of appearance in the Fibonacci sequenceinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleSequências (Matemática)Equações integraisCálculo integralengreponame:Repositório Institucional da UnBinstname:Universidade de Brasília (UnB)instacron:UNBORIGINALARTIGO_OnIntegerNumbers.pdfARTIGO_OnIntegerNumbers.pdfapplication/pdf468033http://repositorio2.unb.br/jspui/bitstream/10482/12760/1/ARTIGO_OnIntegerNumbers.pdffe92280659457eb2d1daa9bd125947eeMD51open accessLICENSElicense.txtlicense.txttext/plain257http://repositorio2.unb.br/jspui/bitstream/10482/12760/2/license.txte82f6f4dc714378dcc5f85c2618b2897MD52open accessTEXTARTIGO_OnIntegerNumbers.pdf.txtARTIGO_OnIntegerNumbers.pdf.txtExtracted texttext/plain9506http://repositorio2.unb.br/jspui/bitstream/10482/12760/3/ARTIGO_OnIntegerNumbers.pdf.txt8f98bbe9e0b098f830a0fedc508de61dMD53open access10482/127602023-05-26 21:16:56.089open accessoai:repositorio.unb.br:10482/12760TGljZW5zZSBncmFudGVkIGJ5IFJpY2FyZG8gVGF2YXJlcyAocmljYXJkb3NvYXJlc0BiY2UudW5iLmJyKSBvbiAyMDEzLTAzLTIyVDIxOjE1OjA0WiAoR01UKToKClN1Ym1pc3PDo28gZWZldGl2YWRhIHBvciBpbnRlZ3JhbnRlIGRhIGVxdWlwZSBkbyBSZXBvc2l0w7NyaW8gSW5zdGl0dWNpb25hbCBkYSBVbkIgZGUgYWNvcmRvIGNvbSBsaWNlbsOnYSBjb25jZWRpZGEgcGVsbyBhdXRvciBlL291IGRldGVudG9yIGRvcyBkaXJlaXRvcyBhdXRvcmFpcy4=Repositório InstitucionalPUBhttps://repositorio.unb.br/oai/requestrepositorio@unb.bropendoar:2023-05-27T00:16:56Repositório Institucional da UnB - Universidade de Brasília (UnB) |
| spellingShingle | On integer numbers with locally smallest order of appearance in the Fibonacci sequence Ferreira, Diego Marques Sequências (Matemática) Equações integrais Cálculo integral |
| status_str | publishedVersion |
| title | On integer numbers with locally smallest order of appearance in the Fibonacci sequence |
| title_full | On integer numbers with locally smallest order of appearance in the Fibonacci sequence |
| title_fullStr | On integer numbers with locally smallest order of appearance in the Fibonacci sequence |
| title_full_unstemmed | On integer numbers with locally smallest order of appearance in the Fibonacci sequence |
| title_short | On integer numbers with locally smallest order of appearance in the Fibonacci sequence |
| title_sort | On integer numbers with locally smallest order of appearance in the Fibonacci sequence |
| topic | Sequências (Matemática) Equações integrais Cálculo integral |
| url | http://repositorio.unb.br/handle/10482/12760 https://dx.doi.org/10.1155/2011/407643 |