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A327983 Run lengths in A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
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, ...
MATHEMATICA
Length /@ Split@ CellularAutomaton[30, {{1}, 0}, {105, {{0}}}] (* Michael De Vlieger, Oct 04 2019 *)
PROG
(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);
A327983(n) = v327983[n];
CROSSREFS
Sequence in context: A023135 A345058 A191654 * A205784 A066272 A237130
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 03 2019
STATUS
approved

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)