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A319606
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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 after a(n-1).
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1
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1, 4, 5, 9, 11, 21, 34, 45, 51, 88, 106, 131, 137, 158, 193, 251, 517, 772, 1029, 1283, 1539, 1794, 2052, 2305, 2561, 4101, 5121, 8197, 10241, 12291, 16388, 20482, 32772, 36865, 49154, 57345, 65539, 262150, 294913, 786437, 851969, 1310724, 1441793, 1835011
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listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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OFF cells outside the triangle of active cells are ignored.
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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 .
0 OFF cell appears for the first time in generation (line) 1, thus a(0) = 1;
1 consecutive OFF cells (0) appear for the first time after line 1 in generation (line) 4, thus a(1) = 4;
2 consecutive OFF cells (00) appear for the first time after (line) 4 in generation (line) 5, thus a(2) = 5. [Corrected by Rémy Sigrist, Jul 06 2020]
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MATHEMATICA
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CellularAutomaton[30, {{1}, 0}, 20000];
(Reverse[Internal`DeleteTrailingZeros[
Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
ls = Table[
Max[Differences[Position[Flatten@{1, %[[n]], 1}, 1]]] - 1, {n, 1,
20000}];
res = {1};
Table[Position[ls, n] // Flatten, {n, 100}];
For[n = 1, n < 40, n++,
AppendTo[res, (Select[%[[n]], # > Last[res] &, 1][[1]])]]
res
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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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