The game begins with a row of $n$ numbers, in increasing order from $1$ to $n$. For example, if $n=7$, we have a row of numbers $(1,2,3,4,5,6,7)$.
On each turn, a player must either remove 1 number, or remove 2 consecutive numbers. For example, the first player to move can remove $2$ or remove 5 and 6 together.
The player who removes the last number wins. Is there a winning strategy for the player who goes first?
p.s. Sorry for the initial confusion. Here are some clarifications. (1) There are two players. (2) Let's say 4 is removed on the first turn. This does NOT make 3, 5 consecutive. So a player can never remove 3 and 5 together.