$k$-Pell-Lucas numbers which are concatenations of two repdigits

Abstract

For any integer $k\ge 2$, let $\{Q_n^{(k)}{\}}_{n\ge -(k-2)}$ denote the $k$-generalized Pell-Lucas sequence which starts with $0,\dots ,2,2$($k$ terms) where each next term is the sum of the $k$ preceding terms. In this paper, we find all the $k$-generalized Pell-Lucas numbers that are concatenations of two repdigits.