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.

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, 333, 123, 181, 69, 200, 279, 372, 117, 188, 212, 122, 137, 263, 576, 96, 149, 225, 169, 150, 276, -1, 304, 281, 106, 215, 160, 206, 197, -1, 359, 221, 355, -1, 447, 178, 314, 431

Offset: 1

Author

Sebastian F. Orellana, Mar 10 2022

Keywords

• sign

Comments

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.

Examples

			For n = 1:
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all cells are dead after one generation, hence a(1)=1.
For n = 2:
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all cells are dead after one generation, hence a(2)=1.
For n = 3:
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a pattern repeats after one generation, hence a(3)=1.
For n = 4:
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. o . o . . | . . o o . . |
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a pattern repeats after one generation, hence a(4) = 1.
For n = 5:
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a pattern begins to oscillate between four parallel "blinkers" after one generation, hence a(5) = 3.
		

Crossrefs

Cf. A089520 (filled square).