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

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

1,4

Comments

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

References

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

Links

Table of n, a(n) for n=1..36.

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

Formula

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

Mathematica

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 *)

Crossrefs

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

Sequence in context: A261882 A021058 A036792 * A335932 A198581 A154735

Adjacent sequences: A334494 A334495 A334496 * A334498 A334499 A334500

Keyword

nonn,more

Author

N. J. A. Sloane, May 05 2020

Extensions

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.

Status

approved