• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

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

Original Article

Unrestricted Mersenne and Mersenne-Lucas Hybrid Sequences

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


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


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© 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)


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