Unrestricted Mersenne and Mersenne-Lucas Hybrid Sequences

D Maheswari; B Malini Devi; S Devibala

doi:10.17485/IJST/v16i41.1726

Article

Unrestricted Mersenne and Mersenne-Lucas Hybrid Sequences

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i41.1726

Year: 2023, Volume: 16, Issue: 41, Pages: 3591-3598

Original Article

Unrestricted Mersenne and Mersenne-Lucas Hybrid Sequences

D Maheswari^1*, B Malini Devi², S Devibala³

¹Research Scholar, School of Mathematics, Madurai Kamaraj University, Madurai, 21, TamilNadu, India
²Guest Lecturer, Department of Mathematics, Sri Meenakshi Government Arts College for Women (A), Madurai, Tamil Nadu, India
³Associate Professor, Department of Mathematics, Sri Meenakshi Government Arts College for Women (A), Madurai, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:12 July 2023, Accepted Date:26 September 2023, Published Date:31 October 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The creation of Unrestricted Mersenne and Mersenne-Lucas Hybrid Sequences is the goal. Methods: Consider Mersenne and Mersenne-Lucas sequences associated with hybrid numbers. Then choosing the coefficients of hybrid numbers as arbitrary to find recurrence relations, generating functions and Binet formulas for the above sequences, and verifying the same through well-known identities. Findings: An infinite number of terms of the unrestricted Mersenne and Mersenne-Lucas hybrid sequences are found. We have verified these sequences through some well-known identities. Novelty: In contrast to the study of Mersenne and Mersenne-Lucas hybrid sequences, where the coefficients of the ordered basis of the subsequent components of the sequences were chosen, here we choose arbitrary coefficients for these sequences.

Keywords: Mersenne Sequence, MersenneLucas Sequence, Hybrid numbers, Unrestricted Sequences, Binet Formula

References

Devi BM, Devibala S. A View on the Mersenne and Mersenne-Lucas Numbers. GIS Science Journal. 2021;8(8):784–789. Available from: https://drive.google.com/file/d/1Umps6-p-rBhwEaPu4RlO_3br7cnsszZj/view
Devi BM, Devibala S. Some Sums Formulae for Products of terms of Mersenne and Mersenne-Lucas Numbers. Adalya Journal. 2021;10(8):74–79. Available from: https://drive.google.com/file/d/1ddR0zSwLbai_Uz7SPMkLiJVNBwp0HzRm/view
Alp Y, Kocer EG. Hybrid Leonardo numbers. Chaos, Solitons & Fractals. 2021;150:111128. Available from: https://doi.org/10.1016/j.chaos.2021.111128
Senturk GTD, Bilgici A, Dasdemir Z, Unal. A Study on Horadam Hybrid Numbers. Turkish Journal of Mathematics. 2020;44(4):1212–1221. Available from: https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=1274&context=math
Liana AS, Wloch I. The Fibonacci hybrid numbers. Utilitasmathematica. 2019;110:3–10. Available from: https://utilitasmathematica.com/index.php/Index/article/view/1428
Kizilates C. A new generalization of Fibonacci hybrid and Lucas hybrid numbers. Chaos, Solitons and Fractals. 2020;130:109449. Available from: https://doi.org/10.1016/j.chaos.2019.109449
Catarino P, Bilgici G. A Note on Modified k-Pell Hybrid Numbers. Konuralp Journal of Mathematics. 2020;8(2):229–233. Available from: https://dergipark.org.tr/en/download/article-file/1042841
Kilic N. On k-Jacobsthal and k-Jacobsthal-Lucas hybrid numbers. Journal of Discrete Mathematical Sciences and Cryptography. 2021;24(4):1063–1074. Available from: https://doi.org/10.1080/09720529.2021.1873253
Szynal-Liana A, Włoch I. On Jacobsthal and Jacobsthal-Lucas Hybrid Numbers. Annales Mathematicae Silesianae. 2019;33(1):276–283. Available from: https://intapi.sciendo.com/pdf/10.2478/amsil-2018-0009
Szynal-Liana A, Wloch I. On generalized Mersenne hybrid numbers. Annales Universitatis Mariae Curie-Sklodowska Sectio A. 2020;74(1):77–84. Available from: https://dx.doi.org/10.17951/a.2020.74.1.77-84
Ozkan E, Uysal M. Mersenne-Lucas Hybrid Numbers. Mathematica Montisnigri. 2021;52:17–29. Available from: https://www.montis.pmf.ac.me/allissues/52/Mathematica-Montisnigri-52-2.pdf
Kumari M, Prasad K, Tanti J, Ozkan E. On the properties of r-circulant matrices involving Mersenne and Fermat numbers. International Journal of Nonlinear Analysis and Applications. 2023;14(5):121–131. Available from: https://ijnaa.semnan.ac.ir/article_7504_5ecc40efd66e3a648368063f9973c700.pdf
Eser E, Kuloglu B, Ozcan E. On the Mersenne and Mersenne-Lucas hybrinomial quaternions. Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science. 2023;3(65):129–144. Available from: https://doi.org/10.31926/but.mif.2023.3.65.1.10
Saba N, Boussayoud A, Kanuri KVV. Mersenne Lucas numbers and complete homogeneous symmetric functions. Journal of Mathematics and Computer Science. 2021;24(02):127–139. Available from: http://dx.doi.org/10.22436/jmcs.024.02.04
Chelgham M, Boussayoud A. On the k-Mersenne–Lucas numbers. Notes on Number Theory and Discrete Mathematics. 2021;27(1):7–13. Available from: https://nntdm.net/papers/nntdm-27/NNTDM-27-1-007-013.pdf

Copyright

© 2023 Maheswari et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)