Padovan numbers that are concatenations of two distinct repdigits

Abstract

Let $(P_n{)}_{n\ge 0}$ 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 Padovan numbers that are concatenations of two distinct repdigits.

Accepted manuscript. 9 pages