$k$-Fibonacci numbers that are palindromic concatenations of two distinct Repdigits

Abstract

Let $k\ge 2$ and $\{F_n^{(k)}{\}}_{n\ge 2-k}$ be the sequence of $k$--generalized Fibonacci numbers whose first $k$ terms are $0,\dots ,0,0,1$ and each term afterwards is the sum of the preceding $k$ terms. In this paper, we determine all $k$-Fibonacci numbers that are palindromic concatenations of two distinct repdigits.

14 pages