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

1,5

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.

Links

Table of n, a(n) for n=1..63.

Example

For n = 1:
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. o . | . . . |
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all cells are dead after one generation, hence a(1)=1.
For n = 2:
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. o . . | . . . . |
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all cells are dead after one generation, hence a(2)=1.
For n = 3:
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. o . o .| . . o . . |
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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 . . |
. . o . o . | . o . . o . |
. 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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. . 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 . . | . . . o o o . . . | . . . o o o . . . | . . . . . . . . . |
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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).

Sequence in context: A232092 A345196 A185271 * A158012 A032446 A271563

Adjacent sequences: A352282 A352283 A352284 * A352286 A352287 A352288

Keyword

sign

Author

Sebastian F. Orellana, Mar 10 2022

Status

approved