The game of Huggy Bear is popular at large parties. The emcee gets all of the participants on the dance floor, and then calls out numbers between 2 and 12, inclusive. When a number is called, the players must form into groups of that number. Anyone left over is out. The game continues until there are only 2 people left. They are the winners.

You have written a song for playing this game, which you are planning to record on a CD of party songs. In the song, at certain points, you will pause and call out a number. The players must then form groups of that size. These numbers will be the same each time the song is played.

You would like your CD to be used with groups ranging from 20 up to N participants. You want N as large as possible, always leaving exactly 2 players at the end. How large can N be, and what sequence of numbers should you call? A short sequence is preferred.

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