A094603 a(n) is the length of the maximal sequence of rightmost black cells in the n-th row of Rule 30 (begun from an initial black cell).

1, 3, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 3, 1, 9, 1, 3, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 3, 1, 15, 1, 3, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 3, 1, 9, 1, 3, 1, 4, 1, 3, 1, 6, 1

Offset

1,2

Comments

New numbers (A094604) in the sequence occur at positions 2^m.

References

Wolfram, Stephen. A New Kind of Science, Wolfram Media, 2002.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Eric Rowland, Local nested structure in rule 30, Complex Systems 16 (2006) 239-258.

Eric Weisstein's World of Mathematics, Rule 30

Index entries for sequences related to cellular automata

Formula

Conjecture: a(n) = A094604(A007814(n)). - Alan Michael Gómez Calderón, Feb 17 2023

Example

From Michael De Vlieger, Oct 06 2015: (Start)
First 12 rows, replacing "0" with ".", ignoring "0" outside of range of 1's, for better visibility of ON cells, the number of contiguous rightmost black cells in each row appears at left:
1                          1
3                        1 1 1
1                      1 1 . . 1
4                    1 1 . 1 1 1 1
1                  1 1 . . 1 . . . 1
3                1 1 . 1 1 1 1 . 1 1 1
1              1 1 . . 1 . . . . 1 . . 1
6            1 1 . 1 1 1 1 . . 1 1 1 1 1 1
1          1 1 . . 1 . . . 1 1 1 . . . . . 1
3        1 1 . 1 1 1 1 . 1 1 . . 1 . . . 1 1 1
1      1 1 . . 1 . . . . 1 . 1 1 1 1 . 1 1 . . 1
4    1 1 . 1 1 1 1 . . 1 1 . 1 . . . . 1 . 1 1 1 1
1  1 1 . . 1 . . . 1 1 1 . . 1 1 . . 1 1 . 1 . . . 1
(End)

Mathematica

rows = 105; ca = CellularAutomaton[30, {{1}, 0}, rows-1]; a[n_] := Length[ Last[ Split[ ca[[n, rows-n+1 ;; rows+n-1]]]]]; Table[ a[n], {n, 1, rows}] (* Jean-François Alcover, Oct 11 2012 *)
Length /@ Map[Last, Split /@ CellularAutomaton[30, {{1}, 0}, 120] /. 0 -> Nothing /. {} -> Nothing] (* Michael De Vlieger, Oct 06 2015 *)

Crossrefs

Cf. A007814, A094604.

Sequence in context: A116992 A233267 A090740 * A165595 A213181 A301848

Adjacent sequences: A094600 A094601 A094602 * A094604 A094605 A094606

Keyword

easy,nice,nonn

Author

Eric Rowland, May 13 2004

Status

approved