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Coordinates X_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).
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%I #13 Oct 27 2019 11:15:21

%S 0,2,4,7,8,11,12,14,16,18,21,24,26,28,29,31,32,34,36,38,40,42,43,45,

%T 46,48,49,51,54,55,57,60,61,63,64,66,68,71,72,74,75,77,80,81,83,86,87,

%U 89,92,93,95,97,98,100,103,104,106,108,109

%N Coordinates X_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

%C We study Maharaja Nim on the square spiral, as in A307282, A307283, and in particular the P-positions in the 4th quadrant. As in A140100 and A140101 (which are the analogs if we use a Queen instead of a Maharaja) we take the X-axis to point South and the Y-axis to point East.

%C The P-positions now lie on two roughly straight lines, with coordinates (X_upper(n), Y_upper(n)) with X_upper(n) <= Y_upper(n), and (X_lower(n), Y_lower(n)) with X_lower(n) <= Y_lower(n). These four sequences are A307284-A307287.

%C The two lines are the hard-to-see black pixels in the fourth quadrant in the Sigrist illustration.

%H Rémy Sigrist, <a href="/A307282/a307282_1.png">Colored representation of the spiral for x = -500..500 and y = -500..500</a> (where the hue is function of T(x,y) and black pixels correspond to 0's)

%Y Cf. A140100, A140101, A307282, A307283, A307284-A307287.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Apr 08 2019