Problem

Source: ONEM 2017 Peruvian Mathematics Olympiad 2017

Tags: number theory



A sequence infinity $a_{1}, a_{2},...,$ is $generadora$ if: $a_{1}=1,2$ and $a_{n+1}$ is obtained by placing a digit 1 on the left or a digit 2 on the right for all natural n. Prove that there is an infinite $generadora$ sequence such that it does not contain any multiples of 7.