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In this paper, we study and investigate the k-Mersenne and k-Mersenne-Lucas sedenions. We give their algebraic properties in closed form and present some well-known identities such as Catalan’s identity, d’Ocagne’s identity, Vajda’s identity, etc. Moreover, for these sedenions we present ordinary and exponential generating functions and series sum formulas. In particular for \(k=1\) , the results are presented for Mersenne and Mersenne-Lucas sedenions.

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Sedenion Algebra of the k-Mersenne and k-Mersenne-Lucas Numbers

  • 会议论文

  • 发表日期：

    2025年

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  • Kalika Prasad,
  • Munesh Kumari

摘要

In this paper, we study and investigate the k-Mersenne and k-Mersenne-Lucas sedenions. We give their algebraic properties in closed form and present some well-known identities such as Catalan’s identity, d’Ocagne’s identity, Vajda’s identity, etc. Moreover, for these sedenions we present ordinary and exponential generating functions and series sum formulas. In particular for \(k=1\) , the results are presented for Mersenne and Mersenne-Lucas sedenions.