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.2021.27.1.101111
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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 TrasosMontes 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 lefthand side, and two more generating matrices of Oresme for the righthand 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
References
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Corrigendum
 Mangueira, M. C. dos S., Vieira, R. P. M., Alves, F. R. V., & Catarino, P. M. M. (2021). Corrigendum to “The Oresme sequence: The generalization of its matrix form and its hybridization process” [Notes on Number Theory and Discrete Mathematics, Vol. 27, 2021, No. 1, 101–111]. Notes on Number Theory and Discrete Mathematics, 27(4), 276279.
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Cite this paper
Mangueira, M. C. dos S., Vieira, R. P. M., Alves, F. R. V., & Catarino, P. M. M. (2021). The Oresme sequence: The generalization of its matrix form and its hybridization process. Notes on Number Theory and Discrete Mathematics, 27(1), 101111, doi: 10.7546/nntdm.2021.27.1.101111.