Some Identities of Dual Mersenne Numbers - Nukran, Semra Kaya; Gürgil, İbrahim (Communications in Mathematics and Applications, 2022)
The aim of this paper is to introduce the dual forms of the Mersenne, Jacobsthal and Jacobsthal-Lucas numbers which are called dual Mersenne, dual Jacobsthal and dual Jacobsthal-Lucas numbers. We give the widely known identities like, Binet to generalize these sequences, Catalan, and Cassini identities along with some useful properties of these dual sequences. We also show that identities of the dual forms of these sequences have a strong relation with their identities in their normal forms. We added the negative subscripts of dual Mersenne numbers. Finally, we show the relation of dual Mersenne numbers with dual Jacobsthal and dual Jacobsthal-Lucas numbers.