3. and play a game, given an integer , writes down first, then every player sees the last number written and if it is then in his turn he writes or , but his number cannot be bigger than . The player who writes wins!, For wich values of does wins?
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3. $A$ and $B$ play a game, given an integer $N$, $A$ writes down $1$ first, then every player sees the last number written and if it is $n$ then in his turn he writes $n+1$ or $2n$, but his number cannot be bigger than $N$. The player who writes $N$ wins!, For wich values of $N$ does $B$ wins?
Izvor: Međunarodna matematička olimpijada, shortlist 2004
Školjka 
and 
play a game, given an integer 
, 
first, then every player sees the last number written and if it is 
then in his turn he writes 
or 
, but his number cannot be bigger than