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A319780
a(n) is the period of cyclic structures that appear in the 3-state (0,1,2) 1D cellular automaton started from a single cell at state 1 with rule n.
0
2, 2, 1, 0, 2, 1, 0, 2, 1, 2, 0, 1, 0, 0, 2, 0, 0, 1, 2, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 0, 2, 1, 0, 2, 1
OFFSET
1,1
COMMENTS
The length of the sequence is equal to 3^3^3 = 7625597484987.
EXAMPLE
1D cellular automaton with rule=1 gives the following generations:
1 ..........1.......... <------ start
2 111111111...111111111 <------ end
3 ..........1..........
4 111111111...111111111
5 ..........1..........
6 111111111...111111111
7 ..........1..........
The period is 2, thus a(1) = 2.
For rule=150:
1 ..........1..... <------ start
2 .........22..... <------ end
3 ........1.......
4 .......22.......
5 ......1.........
6 .....22.........
7 ....1...........
The period is 2, thus a(150) = 2.
For rule=100000000797:
1 .........1....... <------ start
2 ........2.2......
3 ........111......
4 .......2.112.....
5 .......12........
6 ......21.........
7 ........2........ <------ end
8 ........1........
9 .......2.2.......
10 .......111.......
11 ......2.112......
12 ......12.........
13 .....21..........
14 .......2.........
15 .......1.........
The period is 7, thus a(100000000797) = 7.
a(10032729) = 12.
a(10096524) = 16.
MATHEMATICA
Table[
Length[
Last[
FindTransientRepeat[(Internal`DeleteTrailingZeros[
Reverse[Internal`DeleteTrailingZeros[#]]]) & /@
CellularAutomaton[{i, 3}, {ConstantArray[0, 25], {1}, ConstantArray[0, 25]} // Flatten, 50], 2]]],
{i, 1, 1000}
]
CROSSREFS
Cf. A180001.
Sequence in context: A287150 A257109 A096830 * A141647 A366386 A358729
KEYWORD
nonn,fini
AUTHOR
Philipp O. Tsvetkov, Sep 27 2018
STATUS
approved