The finitude of the periodic points of the Conway ordered sequence

Authors

DOI:

https://doi.org/10.5902/2179460X70592

Keywords:

Fixed point, Function, Sequence, Orbit

Abstract

In this paper, we present some properties of the Conway ordered sequence or  counting sequence. Such properties are related to orbits and fixed points. Our main result is to determine a limitation for the number of digits in the orbit of any natural number x, that is, starting with any finite initial term, the sequence terms will have a length limited to a maximum of 21 digits, and therefore the orbits are relatively periodics.

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Author Biographies

Eudes Antonio Costa, Universidade Federal do Tocantins, Arraias, TO

Licenciado em Matemática pela Universidade Federal de Goiás, doutor em Matemática pela Universidade de Brasília, docente da Universidade Federal do Tocantins, Arraias, Matemática.

Fernando Soares de Carvalho, Universidade Federal do Tocantins, Arraias, TO

Doutor em Ciências Mecânicas pela Faculdade de Tecnologia, UnB (2020). Mestre em Matemática pela Universidade Federal de Goiás (2011). Especialização em Matemática e Estatística pela Universidade Federal de Lavras - MG (2009) . Possui graduação em Matemática pela Universidade Federal de Goiás (2003). Foi Professor efetivo da Universidade Estadual de Goiás (2010), da Faculdade de Ceres (FACERES) (2008-2010), da Universidade Federal de Goiás (2005-2008), da rede pública de ensino do Estado de Goiás (2004-2010). Atualmente é professor efetivo (Adjunto IV) da Universidade Federal e Docente vinculado ao Mestrado Profissional em Matemática (PROFMAT).

Élis Gardel da Costa Mesquita, Universidade Federal do Tocantins, Arraias, TO

Possui graduação (bacharel) em Matemática pela Universidade Federal de Goiás (2009), mestrado em Matemática pela Universidade de Brasília (2011) e doutorado em Matemática pela Universidade de Brasília (2019). Atualmente é professor adjunto da Universidade Federal do Tocantins. Tem experiência na área de Matemática, com ênfase em Matemática aplicada e Ensino de Matemática.

References

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MANERO GARCÍA, et al. Diseño e implementación de tareas de alta demanda cognitiva basadas en la sucesión look and say. Avances de investigación en educación matemática, [s.l.], n. 20, p. 161-183, 2021.

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OBMEP:BRASIL. Banco de Questões 2017. OBMEP - Olimpíada Brasileira de Matemática das Escolas Públicas, Sociedade Brasileira de Matemática. [S.l]: IMPA, 2017. Disponível em: www.obmep.org.br. Acesso em: 31/05/2022.

SLOANE, N. J., et al. The on-line encyclopedia of integer sequences. 2003. Disponível em: http://oeis.org/A005151. Acesso em: 31/05/2022.

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Published

2022-12-19

How to Cite

Antonio Costa, E. A., Soares de Carvalho, F. S. de, & Gardel da Costa Mesquita, Élis G. da C. (2022). The finitude of the periodic points of the Conway ordered sequence. Ciência E Natura, 44, e58. https://doi.org/10.5902/2179460X70592

Issue

Vol. 44 (2022): Continuous Publication

Section

Mathematics

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