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A109630 The winning position when playing the "eeny meeny miny moe" game with n players and eliminating every 8th player. 2
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.

CROSSREFS

Sequence in context: A214747 A110766 A166314 * A201439 A202511 A080094

Adjacent sequences:  A109627 A109628 A109629 * A109631 A109632 A109633

KEYWORD

nonn,easy

AUTHOR

Sergio Pimentel, Aug 02 2005

EXTENSIONS

Edited by Charles R Greathouse IV, Nov 11 2009

STATUS

approved

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Last modified October 27 17:15 EDT 2020. Contains 338035 sequences. (Running on oeis4.)