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A327983
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Run lengths in A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.
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6
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2, 1, 3, 2, 2, 3, 1, 1, 2, 2, 1, 2, 3, 1, 1, 1, 3, 2, 3, 1, 1, 1, 1, 1, 2, 4, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 4, 4, 3, 1, 1, 1, 1, 3, 5, 1, 2, 1, 1, 2, 3, 3, 3, 2, 1, 2, 1, 2, 1, 1, 7, 1, 3, 5, 1, 3, 1, 1, 2, 3, 3, 3, 1, 1, 1, 3, 5, 2, 2, 1, 3, 2, 2, 4, 2, 6, 6, 7, 1, 2, 2, 1, 1, 2, 1, 3, 5, 1, 1, 2, 3, 2
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The evolution of one-dimensional cellular automaton rule 30 proceeds as follows, when started from a single alive (1) cell:
0: (1)
1: 1(1)1
2: 11(0)01
3: 110(1)111
4: 1100(1)0001
5: 11011(1)10111
6: 110010(0)001001
7: 1101111(0)0111111
8: 11001000(1)11000001
9: 110111101(1)001000111
10: 1100100001(0)1111011001
11: 11011110011(0)10000101111
12: 110010001110(0)110011010001
13: 1101111011001(1)1011100110111
When noting up the lengths of consecutive identical values ("runs") in its central column (indicated here with parentheses), we see that there are two ones at first, followed by one zero, followed by three ones, then two zeros, etc, and so we obtain the terms on this sequence: 2, 1, 3, 2, 2, 3, ...
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MATHEMATICA
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Length /@ Split@ CellularAutomaton[30, {{1}, 0}, {105, {{0}}}] (* Michael De Vlieger, Oct 04 2019 *)
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PROG
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(PARI)
up_to = 105;
A269160(n) = bitxor(n, bitor(2*n, 4*n));
A327983list(up_to) = { my(v=vector(up_to), s=1, oc=s, nc, n=0, on=n, k=0); while(k<up_to, n++; s = A269160(s); nc = (s>>n)%2; if(nc!=oc, oc=nc; k++; v[k] = (n-on); on=n)); (v); }
v327983 = A327983list(up_to);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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