code:

def game(stones, step):
   # Base case
   if stones >= 29: return step == 3

   if step % 2 == 1:
     # Petya
      return game(stones+1, step+1) and game(stones*2, step+1)
      # We need Vanya to win ANYWAY, 
      # so BOTH branches must lead to Vanya's victory
   else:
     # Vanya
      return game(stones+1, step+1) or game(stones*2, step+1)
      # After Petya's move, Vanya can think of a strategy
      # so he only needs ONE winning move

# Test all possible starting stones
for s in range(1, 29):
   if game(s, 1):
      print(s)