$k$--Fibonacci numbers with two blocks of repdigits

Abstract

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

arXiv commentThis problem had already been solved by another author, though we were unaware of it