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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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
Eric Rowland, Local nested structure in rule 30, Complex Systems 16 (2006) 239-258.
Eric Weisstein's World of Mathematics, Rule 30
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
Sequence in context: A236386 A066271 A127594 * A108654 A131530 A285379
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

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Last modified April 23 20:33 EDT 2024. Contains 371916 sequences. (Running on oeis4.)