A396116 - OEIS

%I #22 May 20 2026 21:42:21

%S 0,11,17,30,36,47,50,58,59,61,86,89,92,101,116,128,132,138,144,162,

%T 168,180,186,187,191,193,214,239,240,242,244,248,257,276,294,298,300,

%U 302,306,312,318,324,348,360,378,381,384,385,386,391,395,397,404,420,456

%N Consider the square spiral with its cells numbered starting at 0. Four 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 four players.

%H Rémy Sigrist, <a href="/A396116/b396116.txt">Table of n, a(n) for n = 1..10000</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 Jonas Karlsson, <a href="/A396116/a396116.png">Four knights with colors black, red, cyan, purple. Close-up, 200 of each color.</a>

%H Jonas Karlsson, <a href="/A396116/a396116_1.png">Four knights with colors black, red, cyan, purple. Zoom-out, 60K of each color.</a>

%H Scott R. Shannon, <a href="/A396116/a396116_2.png">Four knights with colors Red, Green, Blue, Yellow, after ten million knights have been placed.</a>

%H Rémy Sigrist, <a href="/A396116/a396116.gp.txt">PARI program</a>

%e The spiral begins:

%e      *---*---*---*---*---*---*---*--#1---*--#3

%e      |                                       |

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

%e      |   |                               |   |

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

%e      |   |   |                       |   |   |

%e      *   *   *   *---*---*---*---*   *   *   *

%e      |   |   |   |               |   |   |   |

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

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

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

%e      |   |   |   |   |           |   |   |   |

%e     #4   *   *   *   *---*---*---*   *   *   *

%e      |   |   |   |                   |   |   |

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

%e      |   |   |                           |   |

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

%e      |   |                                   |

%e      *   *---*--#4---*---*---*---*---*---*---*

%e      |

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

%o (PARI) \\ See Links section.

%Y Cf. A392177, A396117, A396118, A396119, A396120, A396121.

%K nonn

%O 1,2

%A _Rémy Sigrist_, May 20 2026