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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 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>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.)