KöMaL 2006 A402

Two players play the following game: Let $n$ be a fixed integer greater than 1. Starting from number $k$=2, each player has two possible moves: either replace the number $k$ by $k$+1 or by 2$k$. The player who is forced to write a number greater than $n$ loses the game. Which player has a winning strategy for which $n$?