A109630 - OEIS

A109630

The winning position when playing the "eeny meeny miny moe" game with n players and eliminating every 8th player.

1, 1, 3, 3, 1, 3, 4, 4, 3, 1, 9, 5, 13, 7, 15, 7, 15, 5, 13, 1, 9, 17, 2, 10, 18, 26, 7, 15, 23, 1, 9, 17, 25, 33, 6, 14, 22, 30, 38, 6, 14, 22, 30, 38, 1, 9, 17, 25, 33, 41, 49, 5, 13, 21, 29, 37, 45, 53, 2, 10, 18, 26, 34, 42, 50, 58, 66, 6, 14, 22, 30, 38, 46, 54, 62, 70, 1, 9, 17, 25

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

OFFSET

1,3

COMMENTS

A version of the Josephus sieve - see for example A000960. - N. J. A. Sloane, May 26 2007

In this game, all the children start standing in front of a chair and the teacher will chant "eeny-meeny-miny-moe..." and eliminate every eighth player, who then has to sit down. The game continues until only one child remains standing. He or she is declared the winner.

The multiples of 8 never appear in this sequence because they are always wiped out in the first round.

LINKS

Table of n, a(n) for n=1..80.

Wikipedia, Eeny, meeny, miny, moe

Index entries for sequences related to the Josephus Problem

FORMULA

For n > 5, if a(n-1) + 8 > n, then a(n) = a(n-1) + 8 - n; otherwise, a(n) = a(n-1) + 8.

EXAMPLE

For n = 4 the winner is the third child because:

1, 2, 3, 4, 1, 2, 3, X (the fourth is eliminated)

1, 2, 3, 1, 2, 3, 1, X (the second is eliminated)

3, 1, 3, 1, 3, 1, 3, X (the first is eliminated, therefore #3 wins); thus a(4)=3.