Tribonacci numbers that are concatenations of two repdigits

Abstract

AbstractLet $$ (T_{n})_{n\ge 0} $$ ( T n ) n ≥ 0 be the sequence of Tribonacci numbers defined by $$ T_0=0 $$ T 0 = 0 , $$ T_1=T_2=1$$ T 1 = T 2 = 1 , and $$ T_{n+3}= T_{n+2}+T_{n+1} +T_n$$ T n + 3 = T n + 2 + T n + 1 + T n for all $$ n\ge 0 $$ n ≥ 0 . In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two repdigits.