A005240 P-positions in Epstein's Put or Take a Square game. (Formerly M3893)

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

1,2

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

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

Table of n, a(n) for n=1..34.

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.

Example

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.

Crossrefs

Cf. A005241, A048760.

Sequence in context: A338126 A360368 A088973 * A147374 A080654 A162690

Adjacent sequences: A005237 A005238 A005239 * A005241 A005242 A005243

Keyword

nonn

Author

N. J. A. Sloane

Status

approved