12.2.12 Number theory

Problem: What is the remainder of the division of \( x_{2018}+ \) \( +x_{2019} \) by 9 , if \( x_{1}=x_{2}=1, x_{2 n+1}=2 x_{2 n}+1 \), \( x_{2 n+2}=x_{1}++x_{2}+\cdots+x_{2 n+1} \).