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%I #69 Sep 10 2023 00:25:07
%S 4,3,12,12,15,16,28,12,29,24,33,33,34,16,12,21,36,43,92,30,32,36,55,
%T 24,30,60,56,46,54,20,48,45,46,74,44,22,58,42,46,26,204
%N Minimum number of live cells in Conway's Game of Life that is a nontrivial oscillator of period n.
%C 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.
%C Most of these terms are only the smallest known values and are not proved to be the minimum. - _Eric M. Schmidt_, Nov 22 2013
%C Which of these terms are actually known? - _Charles R Greathouse IV_, Jun 17 2020
%H LifeWiki, <a href="http://www.conwaylife.com/wiki/Oscillator">Oscillator</a>
%H LifeWiki, <a href="https://www.conwaylife.com/wiki/Rob%27s_p16">Rob's p16</a>
%H LifeWiki, <a href="https://conwaylife.com/wiki/Cribbage">Cribbage</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life">Conway's Game of Life</a>
%e The "blinker" is the smallest period 2 nontrivial oscillator.
%e Its generations have 3 cells:
%e . . . . . | . . . . .
%e . . . . . | . . o . .
%e . o o o . | . . o . .
%e . . . . . | . . o . .
%e . . . . . | . . . . .
%e Therefore a(2) = 3.
%e The "caterer" is the smallest period 3 oscillator.
%e Its generations have 12, 15, and 16 cells:
%e . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . .
%e . . . . o . . . . . . | . . . . . . . o o . . | . . . . . . . . o . .
%e . . o . . . o o o o . | . . . o . o o o o . . | . . . o o o . . . o .
%e . . o . . . o . . . . | . o o o . . o . o . . | . . o o o o o . o . .
%e . . o . . . . . . . . | . . . . . . . . . . . | . . . . o . . . . . .
%e . . . . . o . . . . . | . . . o o . . . . . . | . . . o o . . . . . .
%e . . . o o . . . . . . | . . . . o . . . . . . | . . . o o . . . . . .
%e . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . .
%e Therefore a(3) = 12.
%K nonn,hard,nice,more
%O 1,1
%A _Arkadiusz Wesolowski_, Nov 19 2013
%E a(17) [= 36, Sep 2014 discovery of Merzenich] corrected by _Eric M. Schmidt_, Nov 15 2014
%E a(11) [= 33, Jan 2016 discovery of Dean Hickerson] corrected by _Nathaniel Johnston_, Dec 03 2019
%E a(16) [= 21, Feb 2020 discovery of Rob Liston] corrected by _Oscar Cunningham_, Jun 16 2020
%E a(19)-a(41) from _Sergio Pimentel_, Aug 09 2023