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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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, ...

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 A079336

Adjacent sequences:  A327971 A327972 A327973 * A327975 A327976 A327977

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 03 2019

STATUS

approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)