Repdigits as sums of three Padovan numbers.

Abstract

Let ${\left\{P_n\right\}}_{n\ge 0}$ be the sequence of Padovan numbers defined by $P_0=0$ , $P_1=1=P_2$ , and $P_{n+3}=P_{n+1}+P_n$ for all $n\ge 0$ . In this paper, we find all repdigits in base 10 which can be written as a sum of three Padovan numbers.