Perrin numbers that are concatenations of two repdigits

Abstract Let $$ (P_n)_{n\ge 0}$$ ( P n ) ? 0 be the sequence of Perrin numbers defined by ternary relation P_0=3 = 3 , P_1=0 1 P_2=2 2 and P_{n+3}=P_{n+1}+P_n + for all n\ge 0 . In this paper, we use Baker’s theory nonzero linear forms in logarithms algebraic reduction procedure involving continued fractions, to explicitly determine that are concatenations two repeated digit numbers.