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Search: id:A080595
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| A080595 |
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Consider the standard game of Nim with 3 heaps and make a list of the losing positions (x,y,z) with x <= y <= z in reverse lexicographic order; sequence gives z values. |
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6
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| 0, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 9, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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(x,y,z) is a losing position iff the mod-2 sum of the binary expansions of x,y,z (without carries) is 0.
In this sort the first few triples are: 0 0 0, 0 1 1, 0 2 2, 1 2 3, 0 3 3, 0 4 4, 1 4 5, 0 5 5, 2 4 6, 3 5 6, 0 6 6, 3 4 7, 2 5 7, 1 6 7, 0 7 7, 0 8 8, 1 8 9, 0 9 9, 2 8 10, 3 9 10, 0 10 10, 3 8 11, 2 9 11, 1 10 11, 0 11 11, 4 8 12, 5 9 12, 6 10 12, 7 11 12, 0 12 12. The 0,0,0 triple was added by Joshua Zucker.
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REFERENCES
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I. M. Yaglom, Two games with matchsticks, pp. 1-7 of Qvant Selecta: Combinatorics I, Amer Math. Soc., 2001.
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CROSSREFS
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Cf. A080594, A080593.
A119464, A119465, A119466 give the same terms as these sequences but sorted in a different order (by sum rather than by value of z).
Sequence in context: A061451 A086155 A094606 this_sequence A123579 A005185 A119466
Adjacent sequences: A080592 A080593 A080594 this_sequence A080596 A080597 A080598
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KEYWORD
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easy,nonn
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AUTHOR
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njas, Feb 23 2003
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