# Alan's 3N Game

Alan and Bob are playing with numbers. Starting with the number $$N=1$$ they take turns performing arithmetic manipulations with $$N$$. Alan goes first and always multiplies the current number by $$3$$. Bob adds $$1$$ or $$2$$ to the current number, depending on a coin toss. A number is called reachable, if it can possibly appear in this game. How many reachable numbers are there between $$1$$ and $$1000$$ (inclusive)?

Details and assumptions

Number $$1$$ is considered reachable.

Alan's first step would be to multiply 3 to 1, getting 3, which becomes the current number. Bob then adds either 1 or 2 to the current number (which is 3), depending on the coin toss.

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