A094603 - OEIS

%I #32 Feb 25 2023 02:26:19

%S 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,

%T 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,

%U 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

%N 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).

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

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

%H Michael De Vlieger, <a href="/A094603/b094603.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Rowland, <a href="http://www.complex-systems.com/abstracts/v16_i03_a04.html">Local nested structure in rule 30</a>, Complex Systems 16 (2006) 239-258.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule30.html">Rule 30</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%F Conjecture: a(n) = A094604(A007814(n)). - _Alan Michael Gómez Calderón_, Feb 17 2023

%e From _Michael De Vlieger_, Oct 06 2015: (Start)

%e 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:

%e 1                          1

%e 3                        1 1 1

%e 1                      1 1 . . 1

%e 4                    1 1 . 1 1 1 1

%e 1                  1 1 . . 1 . . . 1

%e 3                1 1 . 1 1 1 1 . 1 1 1

%e 1              1 1 . . 1 . . . . 1 . . 1

%e 6            1 1 . 1 1 1 1 . . 1 1 1 1 1 1

%e 1          1 1 . . 1 . . . 1 1 1 . . . . . 1

%e 3        1 1 . 1 1 1 1 . 1 1 . . 1 . . . 1 1 1

%e 1      1 1 . . 1 . . . . 1 . 1 1 1 1 . 1 1 . . 1

%e 4    1 1 . 1 1 1 1 . . 1 1 . 1 . . . . 1 . 1 1 1 1

%e 1  1 1 . . 1 . . . 1 1 1 . . 1 1 . . 1 1 . 1 . . . 1

%e (End)

%t 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 *)

%t Length /@ Map[Last, Split /@ CellularAutomaton[30, {{1}, 0}, 120] /. 0 -> Nothing /. {} -> Nothing] (* _Michael De Vlieger_, Oct 06 2015 *)

%Y Cf. A007814, A094604.

%K easy,nice,nonn

%O 1,2

%A _Eric Rowland_, May 13 2004