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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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`%I #11 Jul 06 2020 23:01:28
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`%S 1,4,5,9,11,21,34,45,51,88,106,131,137,158,193,251,517,772,1029,1283,
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`%T 1539,1794,2052,2305,2561,4101,5121,8197,10241,12291,16388,20482,
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`%U 32772,36865,49154,57345,65539,262150,294913,786437,851969,1310724,1441793,1835011
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`%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 after a(n-1).
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`%C OFF cells outside the triangle of active cells are ignored.
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`%H Rémy Sigrist, <a href="/A319606/a319606.txt">C program for A319606</a>
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`%e The Rule-30 1D cellular automaton started from a single ON (.) cell generates the following triangle:
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`%e 1 .
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`%e 2 . . .
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`%e 3 . . 0 0 .
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`%e 4 . . 0 . . . .
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`%e 5 . . 0 0 . 0 0 0 .
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`%e 6 . . 0 . . . . 0 . . .
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`%e 7 . . 0 0 . 0 0 0 0 . 0 0 .
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`%e 8 . . 0 . . . . 0 0 . . . . . .
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`%e 9 . . 0 0 . 0 0 0 . . . 0 0 0 0 0 .
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`%e 10 . . 0 . . . . 0 . . 0 0 . 0 0 0 . . .
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`%e 11 . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 .
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`%e 12 . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . .
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`%e 13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 .
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`%e 0 OFF cell appears for the first time in generation (line) 1, thus a(0) = 1;
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`%e 1 consecutive OFF cells (0) appear for the first time after line 1 in generation (line) 4, thus a(1) = 4;
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`%e 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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`%t CellularAutomaton[30, {{1}, 0}, 20000];
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`%t (Reverse[Internal`DeleteTrailingZeros[
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`%t Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
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`%t ls = Table[
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`%t Max[Differences[Position[Flatten@{1, %[[n]], 1}, 1]]] - 1, {n, 1,
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`%t 20000}];
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`%t res = {1};
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`%t Table[Position[ls, n] // Flatten, {n, 100}];
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`%t For[n = 1, n < 40, n++,
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`%t AppendTo[res, (Select[%[[n]], # > Last[res] &, 1][[1]])]]
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`%t res
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`%o (C) See Links section.
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`%Y Cf. A317530.
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`%K nonn
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`%O 0,2
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`%A _Philipp O. Tsvetkov_, Sep 24 2018
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`%E Data corrected and more terms from _Rémy Sigrist_, Jul 06 2020
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