Generalized Lucas Numbers Which are Concatenations of Two Repdigits

A generalization of the well–known Lucas sequence is the k–Lucas sequence with some fixed integer $$k\ge 2$$ . The first k terms of this sequence are $$0,\ldots ,0,2,1$$ , and each term afterwards is the sum of the preceding k terms. In this paper, we find all k–Lucas numbers that are concatenations of two repdigits. This generalizes a prior result which dealt with the above problem for the particular case of Lucas numbers.