A119465 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 y values.

0, 1, 2, 3, 2, 4, 5, 4, 6, 4, 7, 6, 5, 4, 5, 8, 9, 8, 10, 8, 11, 10, 9, 8, 9, 12, 8, 13, 12, 9, 8, 9, 14, 12, 10, 8, 10, 15, 14, 13, 12, 13, 11, 10, 11, 9, 11, 8, 9, 10, 11, 16, 17, 16, 18, 16, 19, 18, 17, 16, 17, 20, 16, 21, 20, 17, 16, 17, 22, 20, 18, 16, 18, 23, 22, 21, 20, 21, 19, 18

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 A080594.

Examples

			The triples with sum <= 20 (this sequence is the second 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

A119464, A119466 give the x and z values; A080593, A080594, A080595 give the same values sorted in a different way.