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%I #20 Nov 09 2018 21:03:00
%S 0,0,2,1,3,1,4,2,5,3,4,4,3,2,4,2,6,4,4,3,5,4,4,3,5,5,4,3,4,4,4,5,8,6,
%T 5,3,5,4,5,3,5,5,5,9,7,5,11,9,7,6,8,6,4,7,5,3,5,6,5,4,4,5,5,3,14,12,
%U 10,8,6,5,4,7,5,6,4,6,4,4,6,4,6,7,5,5,4,4,11,9,7,6,4,6,7,5,7,5,8,6,5
%N Maximum run of white (or OFF) cells in generation n of the Rule 30 elementary cellular automaton.
%H Michael De Vlieger, <a href="/A100053/b100053.txt">Table of n, a(n) for n = 0..5000</a>
%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>
%e From _Michael De Vlieger_, Oct 06 2015: (Start)
%e First 12 rows, replacing "1" with ".", ignoring "0" outside of range of 1's, for better visibility of OFF cells, maximum number of contiguous OFF cells in each row appears at left:
%e 0 .
%e 0 . . .
%e 2 . . 0 0 .
%e 1 . . 0 . . . .
%e 3 . . 0 0 . 0 0 0 .
%e 1 . . 0 . . . . 0 . . .
%e 4 . . 0 0 . 0 0 0 0 . 0 0 .
%e 2 . . 0 . . . . 0 0 . . . . . .
%e 5 . . 0 0 . 0 0 0 . . . 0 0 0 0 0 .
%e 3 . . 0 . . . . 0 . . 0 0 . 0 0 0 . . .
%e 4 . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 .
%e 4 . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . .
%e 3 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 .
%e (End)
%t clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; Max /@ Map[Length@ # &, Map[Split@ # &, Map[clip, CellularAutomaton[30, {{1}, 0}, 98]]] /. 1 -> Nothing, {2}] (* _Michael De Vlieger_, Oct 06 2015 *)
%t CellularAutomaton[30, {{1}, 0}, 100];
%t (Reverse[Internal`DeleteTrailingZeros[
%t Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
%t Table[(Length /@ Select[%[[i]] // Split, Total[#] == 0 &] // Max), {i,
%t 1, % // Length}] /. -\[Infinity] -> 0 (* _Philipp O. Tsvetkov_, Sep 25 2018 *)
%Y Cf. A100054, A100055.
%K nonn
%O 0,3
%A _Eric W. Weisstein_, Oct 31 2004
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