A119464 Consider the standard game of Nim with 3 heaps and make a list of the losing positions (x,y,z) with x <= y <= z sorted by sum, ties broken by putting smallest value of x first, then y, then z; sequence gives x values.

0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 2, 3, 3, 0, 0, 1, 0, 2, 0, 1, 2, 3, 3, 0, 4, 0, 1, 4, 5, 5, 0, 2, 4, 6, 6, 0, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 7, 7, 0, 0, 1, 0, 2, 0, 1, 2, 3, 3, 0, 4, 0, 1, 4, 5, 5, 0, 2, 4, 6, 6, 0, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 7, 7, 0, 8, 0, 1, 8, 9, 9, 0, 2, 8, 10, 10, 0, 1, 2, 3, 3

Offset: 1

Author

Joshua Zucker, May 21 2006

Keywords

• easy
• nonn

Comments

Thanks to Ray Chandler for help in clarifying the relation between this sorted list and the one in A080593.

Examples

			The triples with sum <= 20 (this sequence is the first column) are:
0 0 0
0 1 1
0 2 2
0 3 3
1 2 3
0 4 4
0 5 5
1 4 5
0 6 6
2 4 6
0 7 7
1 6 7
2 5 7
3 4 7
3 5 6
0 8 8
0 9 9
1 8 9
0 10 10
		

Crossrefs

Cf. A119465, A119466 give the y and z values; A080593, A080594, A080595 give the same values sorted in a different way.