Perrin numbers that are palindromic concatenations of two repdigits

TL;DR

This paper characterizes all Perrin numbers that are formed by palindromic concatenations of two repdigits, providing a complete classification of such special numbers within the Perrin sequence.

Contribution

It identifies all Perrin numbers that can be expressed as palindromic concatenations of two repdigits, a novel classification within Perrin numbers.

Findings

Identified all Perrin numbers that are palindromic concatenations of two repdigits.

Provided a complete list or characterization of such Perrin numbers.

Enhanced understanding of the structure of Perrin numbers with specific digit patterns.

Abstract

Let $ \{P_n\}_{n\geq 0} $ be the sequence of Perrin numbers defined by $P_0=3$, $P_1=0$,$P_2=2$ and $P_{n+3}=P_{n+1}+P_{n}$ for all $n \geq 0$. In this paper, we determine all Perrin numbers that are palindromic concatenations of two repdigits.