%I #19 Jun 28 2017 20:29:21

%S 0,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,1,1,

%T 0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,1,0,1,1,1,1,1,0,1,1,1,1,

%U 1,1,1,0,1,1,1,1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0

%N Zero-one sequence based on (3n-2): a(A016777(k))=a(k); a(A007494(k))=1-a(k); a(1)=0.

%C Compare with the generation of the Thue-Morse sequence T=A010060 from T(2n-1)=T(n), T(2n)=1-T(n), T(1)=0.

%C Other zero-one sequences generated in this manner:

%C from triangular numbers: A189011

%C from squares: A188973

%C from pentagonal numbers: A189014

%C from hexagonal numbers: A189212

%C from Beatty [n*sqrt(2)]: A189078 and A189081

%C from cubes: A189008

%C from primes: A189141

%C from (3n): A189215 and A189222

%C from (3n-1): A189097

%C from (3n-2): A188967

%C from (4n): A189289, A189292, A189275, A189298

%H Reinhard Zumkeller, <a href="/A188967/b188967.txt">Table of n, a(n) for n = 1..10000</a>

%e Let u=A016777 and v=A007494, so that u(n)=3n-2 and v=complement(u) for n>=1. Then a is a self-generating zero-one sequence with initial value a(1)=0 and a(u(k))=a(k); a(v(k))=1-a(k).

%e a(2)=a(v(1))=1-a(1)=1

%e a(3)=a(v(2))=1-a(2)=0

%e a(4)=a(u(2))=a(2)=1.

%t u[n_] := 3n - 2; (*A016777*)

%t a[1] = 0; h = 128;

%t c = (u[#1] &) /@ Range[h];

%t d = (Complement[Range[Max[#1]], #1] &)[c]; (*A007494*)

%t Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];

%t Table[a[c[[n]]] = a[n], {n, 1, h}] (*A188967*)

%t Flatten[Position[%, 0]] (*A188968*)

%t Flatten[Position[%%, 1]] (*A188969*)

%o (Haskell)

%o import Data.List (transpose)

%o a188967 n = a188967_list !! (n-1)

%o a188967_list = 0 : zipWith ($)

%o (cycle [(1 -) . a188967, (1 -) . a188967, a188967])

%o (concat $ transpose [[1, 3 ..], [2, 4 ..], [2 ..]])

%o -- _Reinhard Zumkeller_, May 18 2015

%Y Cf. A188968, A188969.

%Y Cf. A257998 (partial sums), A258062 (run lengths).

%K nonn

%O 1

%A _Clark Kimberling_, Apr 14 2011