Repdigits as sums of two generalized Lucas numbers

Abstract

A generalization of the well–known Lucas sequence is the k -Lucas sequence with some fixed integer k ≥ 2. The first k terms of this sequence are 0, . . . , 0, 2, 1, and each term afterwards is the sum of the preceding k terms. In this paper, we determine all repdigits, which are expressible as sums of two k -Lucas numbers. This work generalizes a prior result of Şiar and Keskin who dealt with the above problem for the particular case of Lucas numbers and a result of Bravo and Luca who searched for repdigits that are k -Lucas numbers.