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 A319606 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). 1

%I

%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

%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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Last modified September 21 15:03 EDT 2021. Contains 347598 sequences. (Running on oeis4.)