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

Author

Eric Rowland, May 13 2004

Keywords

• easy
• nice
• nonn

Comments

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

Examples

			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)
		

References

• Stephen Wolfram, 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

Crossrefs

Cf. A007814, A094604.

Programs

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 *)

Formula

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