IMO Shortlist 2004 problem C5

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Dodao/la: arhiva
2. travnja 2012.
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