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