A016741 - OEIS

A016741

Initial pile sizes which guarantee a win for player 2 in a certain variant of Nim.

2, 3, 5, 6, 7, 8, 11, 13, 18, 19, 22, 26, 30, 43, 70, 71, 76, 84, 140, 153, 223, 224, 392, 394, 405, 681, 689, 696, 1149, 1164, 1747, 1759, 1760, 2893, 2894, 2895, 4773, 7316, 7322, 7324, 12418, 12420, 12431, 19052, 19054, 19067

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OFFSET

1,1

COMMENTS

Play starts with a single pile of N > 1 stones. Two players A and B take turns removing stones from the pile.

Player A must remove at least one stone and may remove any number of stones < N on turn A1. On subsequent turns, each player must remove at least one stone and may remove any number of stones not exceeding twice the number of stones removed by their opponent on the previous turn. No player may remove the same number of stones on consecutive turns if there are at least two stones remaining in the pile.

Sequence gives set of initial pile sizes which guarantee a win for B.

LINKS

Table of n, a(n) for n=1..46.

CROSSREFS

Sequence in context: A267300 A063752 A191893 * A191167 A006431 A285528

Adjacent sequences: A016738 A016739 A016740 * A016742 A016743 A016744

KEYWORD

nonn

AUTHOR

John Lame (jlame(AT)imagecafe.com)

EXTENSIONS

More terms from Sean A. Irvine, Jan 19 2019

STATUS

approved