A357950 -id:A357950 - cp's OEIS frontend

A334499 For 0 <= R <= 255, let s(R,n) = eventual period of a single cell in a Rule R cellular automaton operating in a cyclic universe of width n; a(n) = max_R s(R,n).

2, 2, 6, 8, 30, 18, 126, 40, 504, 430, 979, 102, 819, 2198, 6820, 6016, 78812, 7812, 183920, 142580, 352884, 122870, 1630792, 185040, 2777040, 312156, 81688176, 304913, 463347935, 5921860, 1211061438, 26636800, 3315517623, 40012662, 24752893585, 135322524, 40583131393, 535150200, 132932362849, 3936823600

Offset: 1

N. J. A. Sloane, May 05 2020

nonn

			For R = 45, the sequence {s(R,1)..s(R,10)} is 2,2,1,2,30,18,126,2,504,430 (see A334508), and s(45,10) = 430 is the greatest value of any s(R,10), and a(10) = 430.

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020.

Bert Dobbelaere, C++ program
Bradley Klee, Table giving R, then {s(R,1)..s(R,10)} for 0 <= R <= 255
Index entries for sequences related to cellular automata

Cf. A085587, A180001, A334496, A334500-A334515, A357950.

a(n) <= A357950(n). Equality holds for all n <= 35, except n = 12, 13, 23, 24, 25, 26, 28, 34. - Pontus von Brömssen, Nov 09 2022

More terms from Bert Dobbelaere, May 09 2020

A334497 Maximum value of eventual period for any starting configuration for a rule 30 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

1, 1, 1, 8, 5, 1, 63, 40, 171, 15, 154, 102, 832, 1428, 1455, 6016, 10846, 2844, 3705, 6150, 2793, 3553, 38249, 185040, 588425, 312156, 240300, 249165, 1466066, 374265, 2841150, 2002272, 2038476, 5656002, 18480630, 2237472

Offset: 1

N. J. A. Sloane, May 05 2020

Bradley Klee computed a(1)-a(7).

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020.

Dustin Gage, Elizabeth Laub and Briana McGarry, Cellular Automata: Is Rule 30 Random?, 2005.

Cf. A180001, A334496, A334499-A334515, A357950.

a[rule_, init_] := -Subtract @@ Flatten[Map[
     Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[rule],
      init, Unequal, All], {0}]]
tri[n_] := a[30, #] & /@ Tuples[{0, 1}, n];
tri /@ Range[7]
Max /@ %
(* Bradley Klee, Apr 26 2020 *)

a(n) <= A357950(n). Equality holds for n = 4, 8, 16. - Pontus von Brömssen, Oct 22 2022

a(8)-a(12) from Jinyuan Wang, May 14 2020
a(13)-a(22) from Pontus von Brömssen, Oct 22 2022
a(23)-a(36) from Paolo Xausa, Jun 29 2023, using data from Gage, Laub and McGarry (2005), p. 7, Table 2.

cp's OEIS Frontend

A334499 For 0 <= R <= 255, let s(R,n) = eventual period of a single cell in a Rule R cellular automaton operating in a cyclic universe of width n; a(n) = max_R s(R,n).

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