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A327981
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Distances between successive ones 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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1, 2, 1, 1, 3, 1, 4, 2, 1, 3, 3, 1, 1, 2, 2, 1, 1, 3, 1, 1, 2, 2, 2, 1, 5, 1, 3, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 5, 1, 1, 1, 4, 2, 2, 1, 1, 6, 3, 2, 1, 4, 1, 1, 4, 1, 2, 1, 2, 1, 2, 8, 4, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 4, 1, 1, 2, 2, 1, 1, 6, 1, 3, 4, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 2, 1, 1
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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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
The distances between successive 1's in its central column (indicated here with parentheses) are 1-0 (as the first 1 is on row 0, and the second is on row 1), 3-1, 4-3, 5-4, 8-5, 9-8, 13-9, ..., that is, the first terms of this sequence: 1, 2, 1, 1, 3, 1, 4, ...
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MATHEMATICA
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A327981list[upto_]:=Differences[Flatten[Position[CellularAutomaton[30, {{1}, 0}, {upto, {{0}}}], 1]]]; A327981list[300] (* Paolo Xausa, Jun 27 2023 *)
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PROG
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(PARI)
up_to = 105;
A269160(n) = bitxor(n, bitor(2*n, 4*n));
A327981list(up_to) = { my(v=vector(up_to), s=1, n=0, on=n, k=0); while(k<up_to, n++; s = A269160(s); if((s>>n)%2, k++; v[k] = (n-on); on=n)); (v); }
v327981 = A327981list(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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