A327974 a(n) = A051023(n) XOR A051023(n-1), where A051023 gives the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.

0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0

Offset

1

Comments

Taking the first differences of indices of 1's in this sequence gives A327983 from its second term onward.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences related to cellular automata

Index entries for characteristic functions

Formula

a(n) = A051023(n) XOR A051023(n-1).

a(n) = A000035(floor(A327973(n) / A000079(n))).

Example

The evolution of one-dimensional cellular automaton rule 30 proceeds as follows, when started from a single alive (1) cell:
   0:              (1)                         a(n)
   1:             1(1)1                         0
   2:            11(0)01                        1
   3:           110(1)111                       1
   4:          1100(1)0001                      0
   5:         11011(1)10111                     0
   6:        110010(0)001001                    1
   7:       1101111(0)0111111                   0
   8:      11001000(1)11000001                  1
   9:     110111101(1)001000111                 0
  10:    1100100001(0)1111011001                1
  11:   11011110011(0)10000101111               0
  12:  110010001110(0)110011010001              0
  13: 1101111011001(1)1011100110111             1
We start from row 1, and write 0 if the central cell is equal to the central cell in the row above, or 1 if it differs, which gives us terms: 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, ...

Mathematica

A327974list[nmax_]:=BitXor@@@Partition[CellularAutomaton[30, {{1}, 0}, {nmax, {{0}}}], 2, 1]; A327974list[150] (* Paolo Xausa, May 26 2023 *)

Prog

(PARI)
A269160(n) = bitxor(n, bitor(2*n, 4*n)); \\ From A269160.
A110240(n) = if(!n, 1, A269160(A110240(n-1)));
A327973(n) = bitxor(A110240(n), 2*A110240(n-1));
A327974(n) = ((A327973(n)>>n)%2);
(PARI)
up_to = 105;
A269160(n) = bitxor(n, bitor(2*n, 4*n));
A327974list(up_to) = { my(v=vector(up_to), s=1, oc=s, nc, n=0, k=0); while(k<up_to, n++; s = A269160(s); nc = (s>>n)%2; k++; v[k] = bitxor(oc, nc); oc=nc); (v); }
v327974 = A327974list(up_to);
A327974(n) = v327974[n];

Crossrefs

Cf. A000079, A003986, A003987, A110240, A269160, A327973, A327980, A327981, A327983.

Sequence in context: A188321 A257628 A203568 * A286049 A287657 A347198

Adjacent sequences: A327971 A327972 A327973 * A327975 A327976 A327977

Keyword

nonn

Author

Antti Karttunen, Oct 03 2019

Status

approved