A323382 a(n) is the period of the oscillating pattern formed by a diagonal line of 2*n cells in the Life-like cellular automaton B2e3ijkn4cz5/S236.

2, 3, 2, 5, 8, 3, 20, 14, 26, 3, 36, 5, 106, 3, 14, 29, 48, 3, 80, 67, 156, 3, 74, 14, 594, 3, 26, 93, 440, 3, 380, 115, 1062, 3, 1826, 82, 1864, 3, 1488, 2603, 328, 3, 1714, 10229, 2330, 3, 1372, 23, 15202, 3, 43186, 7524, 49534, 3, 69612, 9508, 5112, 3, 1260, 54687

Offset: 1

Author

WG Zeist, Jan 12 2019

Keywords

• nonn

Comments

An explanation of the Hensel notation used to define the cellular automaton rule can be found on the LifeWiki (see links).

Lines of odd lengths are excluded because they break up into patterns not consisting of diagonal lines.

These diagonal line oscillators are effectively emulating a four-state one-dimensional cellular automaton.

From Charlie Neder, Feb 12 2019: (Start)

Specifically, such an oscillator with 2*n cells is isomorphic to a row of 2*n state-1 cells that evolve according to the following rules:

1) A state-1 cell becomes state-3 if it has a state-1 neighbor, and state-2 otherwise,

2) A state-2 cell becomes state-1 unconditionally,

3) A state-3 cell becomes state-1 if both its neighbors are state-3, and state-2 otherwise. (End)

Examples

			a(4) = 5 because a diagonal line of 8 cells oscillates with period 5 in this cellular automaton.
		

Links

• LifeWiki, Isotropic non-totalistic Life-like cellular automaton

Formula

If n == 2 (mod 4), a(n) = 3.