A119465 - OEIS

%I #4 Mar 30 2012 17:36:54

%S 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,

%T 9,14,12,10,8,10,15,14,13,12,13,11,10,11,9,11,8,9,10,11,16,17,16,18,

%U 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

%N 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.

%C Thanks to _Ray Chandler_ for help in clarifying the relation between this sorted list and the one in A080594.

%e The triples with sum <= 20 (this sequence is the second column) are:

%e 0 0 0

%e 0 1 1

%e 0 2 2

%e 0 3 3

%e 1 2 3

%e 0 4 4

%e 0 5 5

%e 1 4 5

%e 0 6 6

%e 2 4 6

%e 0 7 7

%e 1 6 7

%e 2 5 7

%e 3 4 7

%e 3 5 6

%e 0 8 8

%e 0 9 9

%e 1 8 9

%e 0 10 10

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

%K easy,nonn

%O 1,3

%A _Joshua Zucker_, May 21 2006