

A060447


Cyclic tokenpassing 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.


0



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, 11, 14, 7, 7, 11, 11, 11, 11, 19, 20, 11, 11, 11, 11, 14, 14, 22, 17, 17, 17, 16, 14, 14, 16, 20
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OFFSET

1,4


REFERENCES

Suggested by 58th William Lowell Putnam Mathematical Competition, 1997, Problem A2.


LINKS

Table of n, a(n) for n=1..65.
Putnam Mathematical Competitions


EXAMPLE

a(10)=4 because 4 players (numbers 4, 6, 9, 10) remain.


CROSSREFS

Sequence in context: A279401 A168514 A326353 * A268045 A118177 A105069
Adjacent sequences: A060444 A060445 A060446 * A060448 A060449 A060450


KEYWORD

easy,nonn,nice


AUTHOR

SenPeng Eu, Apr 08 2001


STATUS

approved



