cp's OEIS Frontend

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).

%I A094603 #37 Apr 16 2025 05:26:22
%S A094603 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 A094603 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 A094603 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 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).
%C A094603 New numbers (A094604) in the sequence occur at positions 2^m.
%D A094603 Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002.
%H A094603 Michael De Vlieger, <a href="/A094603/b094603.txt">Table of n, a(n) for n = 1..10000</a>
%H A094603 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 A094603 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30</a>
%H A094603 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A094603 Conjecture: a(n) = A094604(A007814(n)). - _Alan Michael Gómez Calderón_, Feb 17 2023
%e A094603 From _Michael De Vlieger_, Oct 06 2015: (Start)
%e A094603 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 A094603 1                          1
%e A094603 3                        1 1 1
%e A094603 1                      1 1 . . 1
%e A094603 4                    1 1 . 1 1 1 1
%e A094603 1                  1 1 . . 1 . . . 1
%e A094603 3                1 1 . 1 1 1 1 . 1 1 1
%e A094603 1              1 1 . . 1 . . . . 1 . . 1
%e A094603 6            1 1 . 1 1 1 1 . . 1 1 1 1 1 1
%e A094603 1          1 1 . . 1 . . . 1 1 1 . . . . . 1
%e A094603 3        1 1 . 1 1 1 1 . 1 1 . . 1 . . . 1 1 1
%e A094603 1      1 1 . . 1 . . . . 1 . 1 1 1 1 . 1 1 . . 1
%e A094603 4    1 1 . 1 1 1 1 . . 1 1 . 1 . . . . 1 . 1 1 1 1
%e A094603 1  1 1 . . 1 . . . 1 1 1 . . 1 1 . . 1 1 . 1 . . . 1
%e A094603 (End)
%t A094603 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 A094603 Length /@ Map[Last, Split /@ CellularAutomaton[30, {{1}, 0}, 120] /. 0 -> Nothing /. {} -> Nothing] (* _Michael De Vlieger_, Oct 06 2015 *)
%Y A094603 Cf. A007814, A094604.
%K A094603 easy,nice,nonn
%O A094603 1,2
%A A094603 _Eric Rowland_, May 13 2004