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.

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.

Links

Table of n, a(n) for n=1..87.

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

Adjacent sequences: A319777 A319778 A319779 * A319781 A319782 A319783

Keyword

nonn,fini

Author

Philipp O. Tsvetkov, Sep 27 2018

Status

approved