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Let $ (P_n)_{n\ge 0}$ be the sequence of Perrin numbers defined by ternaryrelation $ P_0=3 $, $ P_1=0 $, $ P_2=2 $, and $ P_{n+3}=P_{n+1}+P_n $ for all $n\ge 0 $. In this paper, we use Baker's theory for nonzero linear forms inlogarithms of algebraic numbers and the reduction procedure involving thetheory of continued fractions, to explicitly determine all Perrin numbers thatare concatenations of two distinct repeated digit numbers.

Perrin numbers that are concatenations of two distinct repdigits