login
A327981
Distances between successive ones in A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.
6
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
OFFSET
1,2
COMMENTS
First differences of A327984, which gives indices of ones in A051023.
LINKS
FORMULA
a(n) = A327984(1+n) - A327984(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
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, ...
MATHEMATICA
A327981list[upto_]:=Differences[Flatten[Position[CellularAutomaton[30, {{1}, 0}, {upto, {{0}}}], 1]]]; A327981list[300] (* Paolo Xausa, Jun 27 2023 *)
PROG
(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);
A327981(n) = v327981[n];
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 03 2019
STATUS
approved