A190588 Losing positions in Nim (misere) with up to 9 stones on each heap.

1, 22, 33, 44, 55, 66, 77, 88, 99, 111, 123, 145, 167, 189, 246, 257, 347, 356, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 1247, 1256, 1346, 1357, 2222, 2233, 2244, 2255, 2266, 2277, 2288, 2299, 2345, 2367, 2389, 3333, 3344, 3355, 3366, 3377, 3388, 3399, 4444, 4455, 4466, 4477, 4488, 4499, 4567, 4589, 5555, 5566, 5577, 5588, 5599, 6666, 6677, 6688, 6699, 6789, 7777, 7788, 7799, 8888, 8899, 9999, 11111

Offset: 1

Author

Sergio Pimentel, May 13 2011

Keywords

• nonn

Comments

In the game of Nim (misere) the player who takes the last stone loses. This sequence is a subsequence of A009994 (numbers with digits in nondecreasing order).

Examples

			Example: a(2) is 22 because it represents a losing position with two heaps with two stones in each. In the game of Nim (misere) the player who takes the last stone loses. If Player A takes one stone from heap 1, then Player B takes two from heap 2, leaving Player A to pick the last stone and lose the game.
		

Links

• Wikipedia, Nim

Crossrefs

Cf. A009994, A119456, A119464, A119466.