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.

Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences

“…In recent years, many authors have worked on problems involving relations between terms of some binary recurrence sequences and repdigits [9,10,13,17,22]. Some authors extended these problems to the case involving order k generalization of these binary recurrence sequences [1,3,4,6,8,18,24,23]. In fact, in [16], Luca found all repdigits in Lucas sequence whereas in [7], the authors extend this result to the k−Lucas sequences.…”