A327983 Run lengths in A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.

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

Offset: 1

Author

Antti Karttunen, Oct 03 2019

Keywords

• nonn

Examples

			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, ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A051023, A269160, A327974, A327980, A327981, A327984, A327985.

Programs

Mathematica

Length /@ Split@ CellularAutomaton[30, {{1}, 0}, {105, {{0}}}] (* Michael De Vlieger, Oct 04 2019 *)

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(kA269160(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];