MathDB

Eddy and Moor play a game with the following rules:
[*] The game begins with a pile of

N

stones, where

N

is a positive integer. [/*] [*] The

2

players alternate taking turns (e.g. Eddy moves, then Moor moves, then Eddy moves, and so on). [/*] [*] During a player's turn, given

a

stones remaining in the pile, the player may remove

b

stones from the pile, where

\gcd(a,b)=1

and

b\leq a

. [/*] [*] If a player cannot make a move, they lose. [/*]
For example, if Eddy goes first and

N=4

, then Eddy can remove

3

stones from the pile (since

3\leq4

and

\gcd(3,4)=1

), leaving

1

stone in the pile. Moor can then remove

1

stone from the pile (since

1\leq1

and

\gcd(1,1)=1

), leaving

0

stones in the pile. Since Eddy cannot remove stones from an empty pile, he cannot make a move, and therefore loses.
Both Eddy and Moor want to win, so they will both always make the best possible move. If Eddy moves first, for how many values of

N<2016

can Eddy win no matter what moves Moor chooses?

Problem Statement