On Mersenne Numbers and their Bihyperbolic Generalizations

Abstract

In this paper, we introduce Mersenne and Mersenne–Lucas bihyperbolic numbers, i.e. bihyperbolic numbers whose coefficients are consecutive Mersenne and Mersenne–Lucas numbers. Moreover, we study one parameter generalizations of Mersenne and Mersenne–Lucas bihyperbolic numbers. We present some properties of these numbers and relations between them.

Keywords

• 11b37
• 11b39
• mersenne numbers
• recurrence relations
• hyperbolic numbers
• bihyperbolic numbers