Subtraction game of n chips and subtraction set k and k+1

Question

The subtraction game starts with n chips and two players alternate. Players may remove k or k+1 chips, and the winner is the person who makes the last legal move. How would one describe the set of all P positions?

I recognize that all numbers such that x is less than k are P positions, and thus x+k and x+k+1 are N positions, but I don't realize how I could extend this further to generalize the set of P positions.

Answer 1

Positions from $0$ to $k-1$ are losing, positions from $k$ to $2k$ are winning, positions from $2k+1$ to $3k$ are losing etc.

The pattern continues, $k$ losing positions followed by $k+1$ winning positions and so on and so forth.