On $k$-Mersenne and k-Mersenne-Lucas Octonions

Abstract

This paper aims to introduce the k-Mersenne and k-Mersenne-Lucas octonions. We give the closed form formulae for these octonions and obtain some well-known identities like Cassini's identity, d'Ocagne's identity, Catalan identity, Vajda's identity and generating functions of them. As a consequence k = 1 yields all the above properties for Mersenne and Mersenne-Lucas octonions.