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A060447
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Cyclic token-passing numbers with pattern 121: players 1, 2, ..., n are seated around a table. Each has a penny. Player 1 passes a penny to player 2, who passes two pennies to player 3, who passes a penny to player 4. Player 4 passes a penny to player 5, who passes two pennies to player 6, who passes a penny to player 7 and so on, players passing 1,2,1,1,2,1,... pennies to the next player who still has some pennies. A player who runs out of pennies drops out of the game and leaves the table. Sequence gives number of players remaining when game reaches periodic state.
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1
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1, 1, 1, 2, 2, 2, 2, 2, 2, 4, 4, 2, 5, 5, 4, 4, 4, 4, 4, 4, 8, 5, 8, 8, 5, 5, 8, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 17, 17, 14, 7, 7, 11, 11, 11, 11, 19, 20, 20, 11, 11, 11, 14, 14, 22, 17, 17, 17, 16, 14, 14, 16, 20, 16, 10, 16, 17, 20, 20, 20, 23
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OFFSET
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1,4
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REFERENCES
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Suggested by 58th William Lowell Putnam Mathematical Competition, 1997, Problem A-2.
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LINKS
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EXAMPLE
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a(10)=4 because 4 players (numbers 4, 6, 9, 10) remain.
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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EXTENSIONS
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a(41) and a(51) corrected and more terms from Sean A. Irvine, Nov 20 2022
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STATUS
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approved
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