Padovan Numbers as Sum of Two Repdigits

Abstract

Padovan sequence $$(P_{n})$$ is given by $$P_{n}=P_{n-2}+P_{n-3}$$ for $$n\geq3$$ with initial condition $$(P_{0},P_{1},P_{2})=(1,1,1)$$. A positive integer is called a repdigit if all of its digits are equal. In this study, we examine the terms of the Padovan sequence, which are the sum of two repdigits. It is shown that the largest term of the Padovan sequence which can be written as a sum of two repdigits is $$P_{18}=114=111+3.$$