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

Offset: 1

Author

John Lame (jlame(AT)imagecafe.com)

Keywords

• nonn

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.

Extensions

More terms from Sean A. Irvine, Jan 19 2019