The First Study of Mersenne--Leonardo Sequence

Year 2025, Volume: 8 Issue: 1, 11 - 23

Eudes Antonio Costa , Paula Maria Machado Cruz Catarino

https://doi.org/10.33434/cams.1598817

Abstract

In this study, we introduce a new class of numbers, referred to as Modified Mersenne--Leonardo numbers. The aim of this paper is to define the Modified Mersenne--Leonardo sequence and investigate some of its properties, including the recurrence relation, summation formula, and generating function. Additionally, classical identities such as the Tagiuri–Vajda, Catalan, Cassini, and d’Ocagne identities are derived for the Modified Mersenne--Leonardo numbers.

Keywords

Binet’s formula, Generating function, Leonardo numbers, Mersenne numbers, Mersenne--Leonardo numbers

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