

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
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OFFSET

0,2


COMMENTS

The natural number n appears a(n)a(n1) 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 Weisstein's World of Mathematics, Rule 30


EXAMPLE

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



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



