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
Examples
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.
Crossrefs
Cf. A180001.
Programs
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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} ]
Comments