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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.

%I A319780 #23 Dec 25 2018 17:28:53
%S A319780 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,
%T A319780 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,
%U A319780 2,2,2,1,2,2,2,2,2,1,2,2,1,0,2,1,0,2,1
%N 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.
%C A319780 The length of the sequence is equal to 3^3^3 = 7625597484987.
%e A319780 1D cellular automaton with rule=1 gives the following generations:
%e A319780    1  ..........1.......... <------ start
%e A319780    2  111111111...111111111 <------ end
%e A319780    3  ..........1..........
%e A319780    4  111111111...111111111
%e A319780    5  ..........1..........
%e A319780    6  111111111...111111111
%e A319780    7  ..........1..........
%e A319780 The period is 2, thus a(1) = 2.
%e A319780 For rule=150:
%e A319780    1  ..........1..... <------ start
%e A319780    2  .........22..... <------ end
%e A319780    3  ........1.......
%e A319780    4  .......22.......
%e A319780    5  ......1.........
%e A319780    6  .....22.........
%e A319780    7  ....1...........
%e A319780 The period is 2, thus a(150) = 2.
%e A319780 For rule=100000000797:
%e A319780    1  .........1....... <------ start
%e A319780    2  ........2.2......
%e A319780    3  ........111......
%e A319780    4  .......2.112.....
%e A319780    5  .......12........
%e A319780    6  ......21.........
%e A319780    7  ........2........ <------ end
%e A319780    8  ........1........
%e A319780    9  .......2.2.......
%e A319780   10  .......111.......
%e A319780   11  ......2.112......
%e A319780   12  ......12.........
%e A319780   13  .....21..........
%e A319780   14  .......2.........
%e A319780   15  .......1.........
%e A319780 The period is 7, thus a(100000000797) = 7.
%e A319780 a(10032729) = 12.
%e A319780 a(10096524) = 16.
%t A319780 Table[
%t A319780   Length[
%t A319780   Last[
%t A319780    FindTransientRepeat[(Internal`DeleteTrailingZeros[
%t A319780         Reverse[Internal`DeleteTrailingZeros[#]]]) & /@
%t A319780      CellularAutomaton[{i, 3}, {ConstantArray[0, 25], {1}, ConstantArray[0, 25]} // Flatten, 50], 2]]],
%t A319780 {i, 1, 1000}
%t A319780 ]
%Y A319780 Cf. A180001.
%K A319780 nonn,fini
%O A319780 1,1
%A A319780 _Philipp O. Tsvetkov_, Sep 27 2018