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A231427
Minimum number of live cells in Conway's Game of Life that is a nontrivial oscillator of period n.
0
4, 3, 12, 12, 15, 16, 28, 12, 29, 24, 33, 33, 34, 16, 12, 21, 36, 43, 92, 30, 32, 36, 55, 24, 30, 60, 56, 46, 54, 20, 48, 45, 46, 74, 44, 22, 58, 42, 46, 26, 204
OFFSET
1,1
COMMENTS
Oscillators are nontrivial in the sense that there must be at least one cell that oscillates at the full period. See the LifeWiki website for diagrams of these oscillators.
Most of these terms are only the smallest known values and are not proved to be the minimum. - Eric M. Schmidt, Nov 22 2013
Which of these terms are actually known? - Charles R Greathouse IV, Jun 17 2020
LINKS
EXAMPLE
The "blinker" is the smallest period 2 nontrivial oscillator.
Its generations have 3 cells:
. . . . . | . . . . .
. . . . . | . . o . .
. o o o . | . . o . .
. . . . . | . . o . .
. . . . . | . . . . .
Therefore a(2) = 3.
The "caterer" is the smallest period 3 oscillator.
Its generations have 12, 15, and 16 cells:
. . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . .
. . . . o . . . . . . | . . . . . . . o o . . | . . . . . . . . o . .
. . o . . . o o o o . | . . . o . o o o o . . | . . . o o o . . . o .
. . o . . . o . . . . | . o o o . . o . o . . | . . o o o o o . o . .
. . o . . . . . . . . | . . . . . . . . . . . | . . . . o . . . . . .
. . . . . o . . . . . | . . . o o . . . . . . | . . . o o . . . . . .
. . . o o . . . . . . | . . . . o . . . . . . | . . . o o . . . . . .
. . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . .
Therefore a(3) = 12.
CROSSREFS
Sequence in context: A205371 A270633 A272220 * A215942 A054908 A141826
KEYWORD
nonn,hard,nice,more
AUTHOR
EXTENSIONS
a(17) [= 36, Sep 2014 discovery of Merzenich] corrected by Eric M. Schmidt, Nov 15 2014
a(11) [= 33, Jan 2016 discovery of Dean Hickerson] corrected by Nathaniel Johnston, Dec 03 2019
a(16) [= 21, Feb 2020 discovery of Rob Liston] corrected by Oscar Cunningham, Jun 16 2020
a(19)-a(41) from Sergio Pimentel, Aug 09 2023
STATUS
approved