A060447 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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