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A334497
Maximum value of eventual period for any starting configuration for a rule 30 cellular automaton in a cyclic universe of width n.
2
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
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
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