A060447 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.

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

Offset

1,4

References

Suggested by 58th William Lowell Putnam Mathematical Competition, 1997, Problem A-2.

Links

Table of n, a(n) for n=1..73.

Sean A. Irvine Java program (github)

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

Sen-Peng Eu, Apr 08 2001

Extensions

a(41) and a(51) corrected and more terms from Sean A. Irvine, Nov 20 2022

Status

approved