cp's OEIS Frontend

A352285 a(n) is the number of steps in John Conway's game of life that it takes for the smallest square checkerboard pattern with a diagonal of n living cells to either die out or enter a cycle; or -1 if it never cycles.

%I A352285 #81 Mar 22 2022 12:32:30
%S A352285 1,1,1,1,3,4,4,4,40,7,58,9,38,8,37,29,71,55,51,41,49,70,60,93,102,79,
%T A352285 333,123,181,69,200,279,372,117,188,212,122,137,263,576,96,149,225,
%U A352285 169,150,276,-1,304,281,106,215,160,206,197,-1,359,221,355,-1,447,178,314,431
%N A352285 a(n) is the number of steps in John Conway's game of life that it takes for the smallest square checkerboard pattern with a diagonal of n living cells to either die out or enter a cycle; or -1 if it never cycles.
%C A352285 a(n) = -1 iff the pattern's extent grows without bound (since a bounded region must eventually repeat). The first a(n) = -1 is at n=47 where the square launches 8 gliders into open space.
%e A352285 For n = 1:
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%e A352285 all cells are dead after one generation, hence a(1)=1.
%e A352285 For n = 2:
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%e A352285 all cells are dead after one generation, hence a(2)=1.
%e A352285 For n = 3:
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%e A352285 a pattern repeats after one generation, hence a(3)=1.
%e A352285 For n = 4:
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%e A352285 a pattern repeats after one generation, hence a(4) = 1.
%e A352285 For n = 5:
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%e A352285 a pattern begins to oscillate between four parallel "blinkers" after one generation, hence a(5) = 3.
%Y A352285 Cf. A089520 (filled square).
%K A352285 sign
%O A352285 1,5
%A A352285 _Sebastian F. Orellana_, Mar 10 2022