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A294241 Longest non-repeating Game of Life on an n X n torus that ends with a fixed pattern. 0
2, 2, 3, 10, 52, 91 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

We must have a(2n) >= a(n) because one can always place onto a 2n X 2n toroidal board four identical copies of a record-setting pattern for a(n), so that each copy of the pattern "thinks" that it is the sole occupant of an n X n toroidal board and thus acts accordingly. See also comments in A179412 for a related question about the longest repeating pattern on a toroidal board. - Antti Karttunen, Oct 30 2017

LINKS

Table of n, a(n) for n=1..6.

Code Golf Stack Exchange User "Per Alexandersson", Longest non-repeating Game-of-Life sequence

EXAMPLE

For n = 3 the starting state is:

  +---+---+---+

  | * | * | * |

  +---+---+---+

  |   |   |   |

  +---+---+---+

  |   |   |   |

  +---+---+---+

For n = 4 the starting state is:

  +---+---+---+---+

  | * | * | * |   |

  +---+---+---+---+

  |   |   | * |   |

  +---+---+---+---+

  | * | * |   |   |

  +---+---+---+---+

  |   |   |   |   |

  +---+---+---+---+

For n = 5 the starting state is:

  +---+---+---+---+---+

  | * | * |   | * |   |

  +---+---+---+---+---+

  | * |   |   |   |   |

  +---+---+---+---+---+

  | * | * |   | * | * |

  +---+---+---+---+---+

  | * |   | * |   |   |

  +---+---+---+---+---+

  |   |   |   |   |   |

  +---+---+---+---+---+

CROSSREFS

Sequence in context: A338372 A153920 A300483 * A067579 A019143 A084650

Adjacent sequences:  A294238 A294239 A294240 * A294242 A294243 A294244

KEYWORD

nonn,more,hard

AUTHOR

Peter Kagey, Oct 25 2017

STATUS

approved

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Last modified October 5 14:35 EDT 2022. Contains 357258 sequences. (Running on oeis4.)