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.

中文翻译：

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两个Repdigits串联的广义卢卡斯数

众所周知的卢卡斯序列的推广是具有固定整数\(k\ge 2\)的k –卢卡斯序列。这个序列的前k项是\(0,\ldots ,0,2,1\)，之后的每一项都是前面k项的总和。在本文中，我们找到了所有k -Lucas 数，它们是两个 repdigits 的串联。这概括了先前的结果，该结果针对卢卡斯数的特殊情况处理了上述问题。