login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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.

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: A220644 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 02:19 EST 2019. Contains 329108 sequences. (Running on oeis4.)