Repdigits as sums of three balancing numbers

Abstract

Let $ \{B_{n}\}_{n\geq 0} $ be the sequence of Balancing numbers defined by $ B_0=0 $, $ B_1 =1$, and $ B_{n+2}= 6B_{n+1} -B_n$ for all $ n\geq 0 $. In this paper, we find all repdigits in base $ 10 $ which can be written as a sum of three Balancing numbers.