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A147983
A sequence from a 3 X n Chomp game, see the first comment.
1
120, 400, 402, 422, 424, 513, 576, 583, 585, 593, 605, 610, 861, 888, 890, 892, 904, 1013, 1015, 1059, 1129, 1141, 1143, 1163, 1216, 1281, 1291, 1293, 1295, 1419, 1448, 1508, 15231525, 1537, 1561, 1723, 1747, 1824, 1868, 1870, 1875, 1889, 2003, 2010
OFFSET
1,1
COMMENTS
Values of r where a P-position (p,q,r) has a pattern. This algorithm is very efficient. When the length of a period and the start matrix are not of interest (only whether r has or does not have a pattern), the algorithm generates the sequence: 120, 400, 402, ..., 10501, 10583, 10585 very quickly.
First step: generate all the P-positions, where, for example, n = 15000. Second step: run the algorithm.
From Petros Hadjicostas, Apr 11 2020: (Start)
From A. E. Brouwer's website (see below): "Chomp is a game played on a partially ordered set P with smallest element 0. A move consists of picking an element x of P and removing x and all larger elements from P. Whoever picks 0 loses."
"In 3-by-n Chomp, a game position is (p,q,r) with p not less than q and q not less than r.
If r = 0 then this is really 2-by-n Chomp, and the P-positions (previous player wins) are those with p = q+1.
If r = 1, the only P-positions are (3,1,1) and (2,2,1).
If r = 2, the P-positions are those with p = q+2.
If r = 3, the P-positions are (6,3,3), (7,4,3) and (5,5,3).
If r = 4, the P-positions are (8,4,4), (9,5,4), (10,6,4) and (7,7,4).
If r = 5, the P-positions are (10,5,5), (9,6,5) and (a+11,a+7,5) for nonnegative a." (For more details, see his web page.) (End)
LINKS
Emily Bergman, Game theory and an explanation of a 3 x n Chomp! Boards, Senior Mathematics Project, Lynchburg College, 2014. (See also here.)
Andries E. Brouwer, The game of Chomp.
Eva Elduque, The game of CHOMP, Madison Math Circle, Department of Mathematics, UW-Madison.
E. J. Friedman and A. S. Landsberg, Scaling, renormalization, and universality in combinatorial games: The geometry of Chomp, in: A. Dress, Y. Xu, and B. Zhu (eds), Combinatorial Optimization and Applications, COCOA 2007 (Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg).
David Gale, A curious Nim-type game, American Mathematical Monthly 81(8) (1974), 876-879.
Wikipedia, Chomp.
Doron Zeilberger, Three-rowed CHOMP, Advances in Applied Mathematics 26 (2001), 168-179.
Doron Zeilberger, Chomp, recurrences and Chaos(?), Journal of Difference Equations and Applications 10(13-15) (2004), 1281-1293.
KEYWORD
nonn
AUTHOR
Csaba Beretka (bcs183(AT)freemail.hu), Nov 18 2008
EXTENSIONS
Name edited by Petros Hadjicostas, Apr 11 2020
STATUS
approved