The Oresme sequence: The generalization of its matrix form and its hybridization process

Milena Carolina dos Santos Mangueira, Renata Passos Machado Vieira, Francisco Regis Vieira Alves and Paula Maria Machado Cruz Catarino
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 101–111
DOI: 10.7546/nntdm.2021.27.1.101-111
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Authors and affiliations

Milena Carolina dos Santos Mangueira
Department of Mathematics, Federal Institute of Education, Science and Technology
of State of Ceara – IFCE, Treze of Maio, Brazil

Renata Passos Machado Vieira
Department of Mathematics, Federal Institute of Education, Science and Technology
of State of Ceara – IFCE, Treze of Maio, Brazil

Francisco Regis Vieira Alves
Department of Mathematics, Federal Institute of Education, Science and Technology
of State of Ceara – IFCE, Treze of Maio, Brazil

Paula Maria Machado Cruz Catarino
University of Tras-os-Montes and Alto Douro – UTAD
Vila Real, Portugal

Abstract

This article deals with the generalization of the matrix form of the Oresme sequence, extending it to the field of integers. In addition, the two valid generating matrices were discussed, through the permutation of the rows and columns, respectively, totaling two valid matrices of Oresme for the left-hand side, and two more generating matrices of Oresme for the right-hand side. In addition, a new Oresme sequence was introduced, given through the hybridization process of these numbers, obtaining mathematical properties and theorems, inherent to this process.

Keywords

• Matrix form of Oresme
• Oresme’s hybrid numbers
• Oresme sequence

2010 Mathematics Subject Classification

• • 11B37
  • 11B39
  • 11B83

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