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A317530
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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.
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2
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4, 3, 5, 7, 9, 17, 45, 33, 44, 67, 47, 66, 130, 65, 129, 517, 260, 516, 259, 515, 258, 514, 257, 513, 4101, 1025, 4100, 2049, 4099, 16388, 4098, 16387, 4097, 16386, 8193, 16385, 262150, 32769, 262149, 65537, 262148, 131073, 262147, 524291, 262146, 524290, 262145, 524289
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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OFF cells outside the triangle of active cells are ignored.
This is also the position at which n appears for the first time in A100053.
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LINKS
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EXAMPLE
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The Rule-30 1D cellular automaton started from a single ON (.) cell generates the following triangle:
1 .
2 . . .
3 . . 0 0 .
4 . . 0 . . . .
5 . . 0 0 . 0 0 0 .
6 . . 0 . . . . 0 . . .
7 . . 0 0 . 0 0 0 0 . 0 0 .
8 . . 0 . . . . 0 0 . . . . . .
9 . . 0 0 . 0 0 0 . . . 0 0 0 0 0 .
10 . . 0 . . . . 0 . . 0 0 . 0 0 0 . . .
11 . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 .
12 . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . .
13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 .
1 OFF cell (0) appears for the first time in generation (line) 4, thus a(1) = 4;
2 consecutive OFF cells (00) appear for the first time in generation (line) 3, thus a(2) = 3;
5 consecutive OFF cells (00000) appear for the first time in generation (line) 9, thus a(5) = 9;
...
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MATHEMATICA
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CellularAutomaton[30, {{1}, 0}, 10000];
(Reverse[Internal`DeleteTrailingZeros[
Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
Table[Position[(Max@FoldList[If[#2 == 0, #1 + 1, 0] &, 0, #]) & /@ %, i] //
Flatten // First, {i, 1, 29}]
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PROG
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(C) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Data corrected and more terms from Rémy Sigrist, Jul 06 2020
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STATUS
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approved
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