What question did this study set out to answer?

The aim is to determine the conditions under which a linear recurrence sequence contains palindromic concatenations of two repdigits in a base greater than one.

July 19, 2026Open Access

Linear recurrence sequences and palindromic concatenations of two repdigits in base

RLRuofan LiJinan University

Key Points

The aim is to determine the conditions under which a linear recurrence sequence contains palindromic concatenations of two repdigits in a base greater than one.
Defined a linear recurrence relation and established necessary conditions for palindromic concatenations.
Investigated the behavior of sequences and their properties with respect to algebraic integers.
Analyzed the number of terms that meet the palindromic criteria.
Demonstrated that the number of terms fitting the palindromic concatenation criteria is finite.
Defined specific conditions for a non-unit algebraic integer greater than one under which the findings hold.

Abstract

Let β be a non-unit real algebraic integer greater than one and ann≥0 be a sequence satisfying a linear recurrence relation an + 3 = aan+2 + ban+1 + can. Under certain conditions, we prove that the number of an which are palindromic concatenations of two repdigits in base β is finite.

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