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%I #24 Jul 08 2020 20:44:31
%S 4,3,5,7,9,17,45,33,44,67,47,66,130,65,129,517,260,516,259,515,258,
%T 514,257,513,4101,1025,4100,2049,4099,16388,4098,16387,4097,16386,
%U 8193,16385,262150,32769,262149,65537,262148,131073,262147,524291,262146,524290,262145,524289
%N a(n) is that generation of the rule-30 1D cellular automaton started from a single ON cell in which n successive OFF cells appears for the first time.
%C OFF cells outside the triangle of active cells are ignored.
%C This is also the position at which n appears for the first time in A100053.
%H Rémy Sigrist, <a href="/A317530/a317530.txt">C program for A317530</a>
%e The Rule-30 1D cellular automaton started from a single ON (.) cell generates the following triangle:
%e 1 .
%e 2 . . .
%e 3 . . 0 0 .
%e 4 . . 0 . . . .
%e 5 . . 0 0 . 0 0 0 .
%e 6 . . 0 . . . . 0 . . .
%e 7 . . 0 0 . 0 0 0 0 . 0 0 .
%e 8 . . 0 . . . . 0 0 . . . . . .
%e 9 . . 0 0 . 0 0 0 . . . 0 0 0 0 0 .
%e 10 . . 0 . . . . 0 . . 0 0 . 0 0 0 . . .
%e 11 . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 .
%e 12 . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . .
%e 13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 .
%e 1 OFF cell (0) appears for the first time in generation (line) 4, thus a(1) = 4;
%e 2 consecutive OFF cells (00) appear for the first time in generation (line) 3, thus a(2) = 3;
%e 5 consecutive OFF cells (00000) appear for the first time in generation (line) 9, thus a(5) = 9;
%e ...
%t CellularAutomaton[30, {{1}, 0}, 10000];
%t (Reverse[Internal`DeleteTrailingZeros[
%t Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
%t Table[Position[(Max@FoldList[If[#2 == 0, #1 + 1, 0] &, 0, #]) & /@ %, i] //
%t Flatten // First, {i, 1, 29}]
%o (C) See Links section.
%Y Cf. A100053.
%K nonn
%O 1,1
%A _Philipp O. Tsvetkov_, Jul 30 2018
%E a(30)-a(36) from _Robert G. Wilson v_, Aug 07 2018
%E Data corrected and more terms from _Rémy Sigrist_, Jul 06 2020
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