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Revision History for A005240
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
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COMMENTS
The game is played with two layers players alternatingly removing or adding chips on a heap. If C denotes the number of chips on the heap, a player must either put or take the largest possible square number of chips in his move, C -> C +- A048760(C). The player capable of taking all chips wins. The P positions are numbers of chips where the player to draw first will lose (assuming the opponent has a full analysis of the game). - R. J. Mathar, May 06 2016
LINKS
E. R. Berlekamp, J. H. Conway, R. K. Guy, <a href="http://dx.doi.org/10.1007/978-3-322-83172-9">Gewinnen (Strategien fur mathematische Spiele)</a>, Vieweg, (1986) p . 58.
R. K. Guy, <a href="/A005240/a005240.pdf">Letter to N. J. A. Sloane, Aug 1975</a>.
EXAMPLE
5 is in the list a term because either putting 4 or taking 4 leads to squares (9 or 1) and the opponent wins by taking.
20 is in the list a term because either putting 16 or taking 16 leads to squares (36 or 4) and the opponent wins by taking.
AUTHOR
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editing
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approved
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COMMENTS
From _The game is played with two layers alternatingly removing or adding chips on a heap. If C denotes the number of chips on the heap, a player must either put or take the largest possible square number of chips in his move, C -> C +- A048760(C). The player capable of taking all chips wins. The P positions are numbers of chips where the player to draw first will lose (assuming the opponent has a full analysis of the game). - _R. J. Mathar_, May 06 2016: (Start)
The game is played with two layers alternatingly removing or adding chips on a heap. If C denotes the number of chips on the heap, a player must either put or take the largest possible square number of chips in his move, C -> C +- A048760(C). The player capable of taking all chips wins. The P positions are numbers of chips where the player to draw first will lose (assuming the opponent has a full analysis of the game). (End)
STATUS
proposed
editing
STATUS
editing
proposed