A396167 - OEIS

%I #44 May 24 2026 21:47:51

%S 0,17,23,36,40,83,110,119,144,148,156,169,181,194,206,212,229,255,270,

%T 273,289,311,324,326,340,342,346,394,396,414,422,424,455,479,483,502,

%U 514,531,545,563,572,576,598,613,627,641,666,668,670,700,712,714,737

%N Consider the square spiral with its cells numbered starting at 0. Seven players take turns and place knights at the smallest unoccupied cell not attacked by an existing knight of a different player. Sequence lists squares occupied by the first player.

%C A variant of A392177 with seven players.

%H Rémy Sigrist, <a href="/A396167/b396167.txt">Table of n, a(n) for n = 1..10000</a>

%H Azeez Daoud, <a href="https://azeezda.github.io/spiral-knight/">Spiral Knight</a>, Website for displaying up to 8 knights with different step sizes and colors on the square spiral board.

%H Azeez Daoud, <a href="https://github.com/AzeezDa/spiral-knight">Source code for above program</a>

%H Brady Haran, Jonas Karlsson, and N. J. A. Sloane, <a href="https://youtu.be/UiX4CFIiegM">Red & Black Knights (extraordinary result)</a>; <a href="https://youtu.be/VgmDuBCayPw">Amazing Chessboard Patterns (extra)</a>, YouTube Numberphile videos, May 2026.

%H Scott R. Shannon, <a href="/A396167/a396167.png">Seven knights with colors red, green, blue, yellow, purple, orange, grey, after ten million knights have been placed.</a>

%H Scott R. Shannon, <a href="/A396167/a396167_1.png">Seven knights with colors red, green, blue, yellow, purple, orange, grey, after 75 million knights have been placed.</a>

%H Rémy Sigrist, <a href="/A396167/a396167.gp.txt">PARI program</a>

%e The spiral begins:

%e     #4---*--#5---*---*--#2---*---*---*--#7---*

%e      |                                       |

%e      *  #2--#4--#2---*--#3--#7---*--#5--#3  #7

%e      |   |                               |   |

%e      *   *  #1---*---*---*---*--#3--#7  #4   *

%e      |   |   |                       |   |   |

%e      *   *  #2  #4---*---*---*---*  #3   *   *

%e      |   |   |   |               |   |   |   |

%e     #2   *  #5  #1  #2--#4--#3   *   *  #7   *

%e      |   |   |   |   |       |   |   |   |   |

%e      *   *   *   *   *  #1--#2   *  #3   *  #4

%e      |   |   |   |   |           |   |   |   |

%e     #6   *  #1   *   *---*---*---*   *  #7   *

%e      |   |   |   |                   |   |   |

%e      *  #6  #6  #5---*--#2--#1---*--#6   *  #1

%e      |   |   |                           |   |

%e     #6   *  #7---*---*--#5--#6--#2---*--#4   *

%e      |   |                                   |

%e      *  #6---*---*---*---*---*---*--#6---*--#5

%e      |

%e     #1---*--#3---*--#5--#6---*--#6---*--#1---*

%o (PARI) \\ See Links section.

%Y Cf. A392177, A396168, A396169, A396170, A396171, A396172, A396173, A396174, A396175.

%K nonn

%O 1,2

%A _Rémy Sigrist_, May 23 2026.