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%I M3893 #32 Oct 27 2023 10:02:00
%S 0,5,20,29,45,80,101,116,135,145,165,173,236,257,397,404,445,477,540,
%T 565,580,585,629,666,836,845,885,909,944,949,954,975,1125,1177
%N P-positions in Epstein's Put or Take a Square game.
%C The game is played with two 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
%D R. K. Guy, Unsolved Problems in Number Theory, E26.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H 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.
%H R. K. Guy, <a href="/A005240/a005240.pdf">Letter to N. J. A. Sloane, Aug 1975</a>.
%e 5 is a term because either putting 4 or taking 4 leads to squares (9 or 1) and the opponent wins by taking.
%e 20 is a term because either putting 16 or taking 16 leads to squares (36 or 4) and the opponent wins by taking.
%Y Cf. A005241, A048760.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
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