A005240 P-positions in Epstein's Put or Take a Square game.

0, 5, 20, 29, 45, 80, 101, 116, 135, 145, 165, 173, 236, 257, 397, 404, 445, 477, 540, 565, 580, 585, 629, 666, 836, 845, 885, 909, 944, 949, 954, 975, 1125, 1177

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

Examples

			5 is a term because either putting 4 or taking 4 leads to squares (9 or 1) and the opponent wins by taking.
20 is a term because either putting 16 or taking 16 leads to squares (36 or 4) and the opponent wins by taking.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, E26.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• E. R. Berlekamp, J. H. Conway, R. K. Guy, Gewinnen (Strategien fur mathematische Spiele), Vieweg, (1986) p. 58.
• R. K. Guy, Letter to N. J. A. Sloane, Aug 1975.

Crossrefs

Cf. A005241, A048760.