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A094604

Largest number (up to that point) of consecutive rightmost black cells in the rows of Rule 30 (begun from an initial black cell). a(n) = b(2^n), where b(m) is sequence A094603.

1, 3, 4, 6, 7, 9, 15, 16, 24, 25, 27, 29, 34, 36, 37, 39, 41, 43, 48, 49, 51, 54, 55, 58, 60, 63, 64, 66, 69, 70, 72, 74, 77, 79, 80, 82, 84, 86, 90, 91, 93, 100, 103

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OFFSET

0,2

COMMENTS

The natural number n appears a(n)-a(n-1) times in A094606.

The number of contiguous black or ON cells, rightmost or otherwise, includes the terms {10, 11}. Row 42 contains 10 contiguous ON cells right of center, row 45 contains 11 contiguous ON cells left of center. Are these the only instances of contiguous ON cells that set records that are not rightmost? - Michael De Vlieger, Oct 06 2015

REFERENCES

Wolfram, Stephen, A New Kind of Science, Wolfram Media, 2002.

LINKS

Table of n, a(n) for n=0..42.

Eric Rowland, Local nested structure in rule 30, Complex Systems 16 (2006) 239-258.

Eric Weisstein's World of Mathematics, Rule 30

Index entries for sequences related to cellular automata

EXAMPLE

From Michael De Vlieger, Oct 06 2015: (Start)

First 12 rows, replacing "0" with ".", ignoring "0" outside of range of

1's, for better visibility of ON cells, the number of contiguous

rightmost ON cells of each row appears at left:

1 1

3 1 1 1

1 1 1 . . 1

4 1 1 . 1 1 1 1

1 1 1 . . 1 . . . 1

3 1 1 . 1 1 1 1 . 1 1 1

1 1 1 . . 1 . . . . 1 . . 1

6 1 1 . 1 1 1 1 . . 1 1 1 1 1 1

1 1 1 . . 1 . . . 1 1 1 . . . . . 1

3 1 1 . 1 1 1 1 . 1 1 . . 1 . . . 1 1 1

1 1 1 . . 1 . . . . 1 . 1 1 1 1 . 1 1 . . 1

4 1 1 . 1 1 1 1 . . 1 1 . 1 . . . . 1 . 1 1 1 1

1 1 1 . . 1 . . . 1 1 1 . . 1 1 . . 1 1 . 1 . . . 1

Thus the sequence starts with {1, 3, 4, 6, ...} as these set new records for the number of contiguous rightmost ON cells in each row.

(End)

MATHEMATICA

t = Length /@ Map[Last, Split /@ CellularAutomaton[30, {{1}, 0}, 6000] /. 0 -> Nothing /. {} -> Nothing]; a = {0}; Do[If[t[[n]] > Max@ a, AppendTo[a, t[[n]]]], {n, Length@ t}]; Rest@ a (* Michael De Vlieger, Oct 06 2015 *)

CROSSREFS

Cf. A094603, A094605, A094606.

Sequence in context: A236386 A066271 A127594 * A108654 A131530 A285379

Adjacent sequences: A094601 A094602 A094603 * A094605 A094606 A094607

KEYWORD

nonn,more

AUTHOR

Eric Rowland, May 13 2004; revised Aug 10 2005

EXTENSIONS

More terms from Eric Rowland, Jan 21 2006

a(42) from Eric Rowland, Jul 03 2015

STATUS

approved