RS-SMO 2019 Problem 1

Find all positive integers $n, n>1$ for wich holds : If $a_1, a_2 ,\dots ,a_k$ are all numbers less than $n$ and relatively prime to $n$ , and holds $a_1<a_2<\dots <a_k$ , then none of sums $a_i+a_{i+1}$ for $i=1,2,3,\dots k-1$ are divisible by $3$ .