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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). 0
1, 4, 8, 10, 11, 21, 34, 45, 51, 88, 107, 131, 137, 158, 193, 251, 517, 772, 1029, 1283, 1539, 1794, 2052, 2305, 2561, 4101, 5121, 8197, 10241, 12291, 16388, 20482 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

OFF cells outside the triangle of active cells are ignored.

LINKS

Table of n, a(n) for n=0..31.

EXAMPLE

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) 8, thus a(8) = 8;

MATHEMATICA

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

CROSSREFS

Sequence in context: A310972 A246357 A265378 * A235382 A287201 A310973

Adjacent sequences:  A319603 A319604 A319605 * A319607 A319608 A319609

KEYWORD

nonn,more

AUTHOR

Philipp O. Tsvetkov, Sep 24 2018

STATUS

approved

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Last modified March 30 19:09 EDT 2020. Contains 333127 sequences. (Running on oeis4.)