Let \(k\ge 2\) . Some generalizations of the well-known Fibonacci and Lucas sequences are the k-Fibonacci and k-Lucas sequences, respectively. For these sequences, the first k terms are \(0,\ldots ,0,1\) and \(0,\ldots ,0,2,1\) , respectively, and each term afterward is the sum of the preceding k terms. In this manuscript, our main objective is to find all k-Fibonacci and k-Lucas numbers which are (l, m)-antipalindromic numbers, i.e., numbers with a base 10 representation as follows: \(\begin{aligned} \underbrace{a\cdots a}_{l}\underbrace{b\cdots b}_{m }\underbrace{(10-a)\cdots (10-a)}_{l}. \end{aligned}\)
