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

1,2

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).

Links

Table of n, a(n) for n=1..73.

Wikipedia, Nim

Example

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.

Crossrefs

Cf. A009994, A119456, A119464, A119466.

Sequence in context: A096768 A157529 A165932 * A072041 A067035 A074054

Adjacent sequences: A190585 A190586 A190587 * A190589 A190590 A190591

Keyword

nonn

Author

Sergio Pimentel, May 13 2011

Status

approved