A307282 -id:A307282 - cp's OEIS frontend

A307283 P-positions (indices of 0 values) along the spiral in A307282.

0, 25, 31, 37, 43, 86, 96, 106, 116, 122, 134, 146, 158, 363, 383, 403, 423, 847, 877, 907, 937, 1114, 1148, 1182, 1216, 1529, 1569, 1609, 1649, 2035, 2081, 2127, 2173, 2438, 2488, 2538, 2588, 2821, 2875, 2929, 2983, 3494, 3554, 3614, 3674, 4239, 4305, 4371

Offset: 1

N. J. A. Sloane, Apr 05 2019

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..1409 (-1000 <= x <= 1000 and -1000 <= y <= 1000)
Rémy Sigrist, PARI program for A307283

Cf. A307282.

For coordinates of the two lines of P-positions in the fourth quadrant (the hard-to-see black dots) see A307284-A307287.

PARI
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More terms from Rémy Sigrist, Apr 06 2019

A308201 Sprague-Grundy values for Maharaja Nim on an infinite single-quadrant board scanned by upwards antidiagonals.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 2, 6, 7, 1, 4, 0, 8, 3, 6, 5, 1, 9, 10, 0, 4, 6, 3, 11, 5, 2, 8, 7, 7, 8, 10, 12, 1, 9, 5, 3, 9, 11, 0, 2, 3, 6, 12, 10, 8, 8, 5, 1, 4, 7, 0, 11, 13, 2, 9, 10, 12, 2, 6, 5, 13, 8, 4, 0, 11, 14, 11, 7, 3, 13, 8, 10, 9, 2, 14, 1, 6, 12, 12, 9

Offset: 0

N. J. A. Sloane, Jun 30 2019

A Maharaja combines the moves of a queen and a knight.

If we add 1 to every term we get A274630.

			The Sprague-Grundy values are as follows (this shows the first 7 antidiagonals):
  0,  2,  5,  1,  6,  4,  7, ...
  1,  4,  7,  3,  0,  8, ...
  3,  6,  8, 10,  2, ...
  2,  0,  9,  5, ...
  4,  1, 11, ...
  5,  3, ...
  6, ...
  ...

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Urban Larsson and Johan Wästlund, Maharaja Nim: Wythoff’s Queen meets the Knight, arXiv 1207.0765 [math.CO], 2012.
Urban Larsson and Johan Wästlund, Maharaja Nim: Wythoff’s Queen meets the Knight, Integers: Electronic Journal of Combinatorial Number Theory 14 (2014), #G05.
Rémy Sigrist, Colored representation of the first 1000 antidiagonals (where the hue is function of T(x,y) and black pixels correspond to 0's)
Rémy Sigrist, PARI program for A308201

Cf. A307282.
For the positions of the 0's, see A307281.
The top row of the array is A308882 (or A274632 - 1).
The leading column is A274631 - 1, the main diagonal is A274633 - 1.
A274630 is essentially the same sequence (but with 1 added to every term).

PARI
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See Links section.
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More terms from Rémy Sigrist, Jun 30 2019

A307284 Coordinates X_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Original entry on oeis.org

0, 2, 4, 7, 8, 11, 12, 14, 16, 18, 21, 24, 26, 28, 29, 31, 32, 34, 36, 38, 40, 42, 43, 45, 46, 48, 49, 51, 54, 55, 57, 60, 61, 63, 64, 66, 68, 71, 72, 74, 75, 77, 80, 81, 83, 86, 87, 89, 92, 93, 95, 97, 98, 100, 103, 104, 106, 108, 109

Offset: 0

N. J. A. Sloane, Apr 08 2019

nonn

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

Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)

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

A307287 Coordinates Y_lower(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Original entry on oeis.org

0, 1, 9, 13, 19, 22, 37, 52, 58, 69, 78, 84, 90, 101, 112, 118, 132, 138, 149, 160, 171, 180, 191, 200, 211, 222, 228, 237, 248, 259, 268, 279, 288, 299, 308, 319, 325, 336, 345, 356, 362, 373, 382, 393, 402, 413, 424, 430, 441, 450, 461, 470, 481, 487, 498

Offset: 0

N. J. A. Sloane, Apr 08 2019

nonn

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

Rémy Sigrist, Table of n, a(n) for n = 0..58
Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)

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

More terms from Rémy Sigrist, Apr 09 2019

A307286 Coordinates X_lower(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Original entry on oeis.org

0, 5, 17, 25, 35, 41, 67, 96, 107, 127, 144, 155, 166, 186, 206, 217, 243, 254, 274, 294, 314, 331, 351, 368, 388, 408, 419, 436, 456, 476, 493, 513, 530, 550, 567, 587, 598, 618, 635, 655, 666, 686, 703, 723, 740, 760, 780, 791, 811, 828, 848, 865, 885, 896

Offset: 0

N. J. A. Sloane, Apr 08 2019

nonn

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

Rémy Sigrist, Table of n, a(n) for n = 0..58
Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)

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

More terms from Rémy Sigrist, Apr 09 2019

A307285 Coordinates Y_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Original entry on oeis.org

0, 3, 6, 10, 15, 20, 23, 27, 30, 33, 39, 44, 47, 50, 53, 56, 59, 62, 65, 70, 73, 76, 79, 82, 85, 88, 91, 94, 99, 102, 105, 110, 113, 116, 119, 122, 125, 130, 133, 136, 139, 142, 147, 150, 153, 158, 161, 164, 169, 172, 175, 178, 181, 184, 189, 192, 195, 198, 201

Offset: 0

N. J. A. Sloane, Apr 08 2019

nonn

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

Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)

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

cp's OEIS Frontend

A307283 P-positions (indices of 0 values) along the spiral in A307282.

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A308201 Sprague-Grundy values for Maharaja Nim on an infinite single-quadrant board scanned by upwards antidiagonals.

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PARI

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A307284 Coordinates X_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

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Author

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Comments

Links

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A307287 Coordinates Y_lower(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

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Extensions

A307286 Coordinates X_lower(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A307285 Coordinates Y_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Views

Author

Keywords

Comments

Links

Crossrefs