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A327980
Distances between successive zeros in A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.
6
4, 1, 3, 1, 1, 2, 3, 1, 2, 1, 4, 2, 4, 1, 4, 2, 2, 3, 1, 1, 1, 3, 1, 2, 2, 3, 2, 2, 7, 1, 1, 1, 5, 1, 1, 2, 2, 4, 1, 1, 1, 1, 2, 1, 2, 3, 1, 1, 4, 1, 1, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 6, 4, 2, 1, 4, 1, 1, 4, 2, 4, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 1, 5, 1, 7, 1, 1, 1, 1, 1, 8, 3, 1, 2, 3, 4, 1, 1, 1, 1
OFFSET
1,1
COMMENTS
First differences of A327985, which gives indices of zeros in A051023.
FORMULA
a(n) = A327985(1+n) - A327985(n).
EXAMPLE
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
When noting up the distances between successive 0's in its central column (indicated here with parentheses), we obtain 6-2 (as the first 0 is on row 2, and the second is on row 6), 7-6, 10-7, 11-10, 12-11, ..., that is, the first terms of this sequence: 4, 1, 3, 1, 1, ...
MATHEMATICA
A327980list[upto_]:=Differences[Flatten[Position[CellularAutomaton[30, {{1}, 0}, {upto, {{0}}}], 0]]]; A327980list[300] (* Paolo Xausa, Jun 01 2023 *)
PROG
(PARI)
up_to = 105;
A269160(n) = bitxor(n, bitor(2*n, 4*n));
A327980list(up_to) = { my(v=vector(up_to), s=25, n=2, on=n, k=0); while(k<up_to, n++; s = A269160(s); if(!((s>>n)%2), k++; v[k] = (n-on); on=n)); (v); }
v327980 = A327980list(up_to);
A327980(n) = v327980[n];
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 03 2019
STATUS
approved