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A317530 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. 2
4, 3, 5, 7, 9, 17, 45, 33, 44, 67, 47, 66, 130, 65, 129, 517, 260, 516, 259, 515, 258, 514, 257, 513, 4101, 1025, 4100, 2049, 4099, 16388, 4098, 16387, 4097, 16386, 8193, 16385, 262150, 32769, 262149, 65537, 262148, 131073, 262147, 524291, 262146, 524290, 262145, 524289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

OFF cells outside the triangle of active cells are ignored.

This is also the position at which n appears for the first time in A100053.

LINKS

Table of n, a(n) for n=1..48.

Rémy Sigrist, C program for A317530

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 .

1 OFF cell (0) appears for the first time in generation (line) 4, thus a(1) = 4;

2 consecutive OFF cells (00) appear for the first time in generation (line) 3, thus a(2) = 3;

5 consecutive OFF cells (00000) appear for the first time in generation (line) 9, thus a(5) = 9;

...

MATHEMATICA

CellularAutomaton[30, {{1}, 0}, 10000];

(Reverse[Internal`DeleteTrailingZeros[

      Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;

Table[Position[(Max@FoldList[If[#2 == 0, #1 + 1, 0] &, 0, #]) & /@ %, i] //

   Flatten // First, {i, 1, 29}]

PROG

(C) See Links section.

CROSSREFS

Cf. A100053.

Sequence in context: A059902 A304225 A068982 * A171021 A035427 A257120

Adjacent sequences:  A317527 A317528 A317529 * A317531 A317532 A317533

KEYWORD

nonn

AUTHOR

Philipp O. Tsvetkov, Jul 30 2018

EXTENSIONS

a(30)-a(36) from Robert G. Wilson v, Aug 07 2018

Data corrected and more terms from Rémy Sigrist, Jul 06 2020

STATUS

approved

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Last modified September 18 19:19 EDT 2020. Contains 337172 sequences. (Running on oeis4.)