DE-MO 2014 Problem 3

Given two positive integers $n$ and $k$ , we say that $k$ is $n$ -ergetic if: However the elements of $M=\{1,2,\ldots, k\}$ are coloured in red and green, there exist $n$ not necessarily distinct integers of the same colour whose sum is again an element of $M$ of the same colour. For each positive integer $n$ , determine the least $n$ -ergetic integer, if it exists.