%I #9 Oct 20 2017 14:21:46

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

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

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

%N Zero-one sequence based on the sequence floor(n*sqrt(2)): a(A001951(k))=a(k); a(A001952(k))=1-a(k); a(1)=0, a(2)=0.

%H G. C. Greubel, <a href="/A189078/b189078.txt">Table of n, a(n) for n = 1..10000</a>

%e Let u=A001951=(Beatty sequence for sqrt(2)) and v=A001952=(Beatty sequence for 2+sqrt(2)). Then A189078 is the sequence a given by a(u(k))=a(k); a(v(k))=1-a(k), where a(0)=0 and a(1)=0.

%t r = 2^(1/2); u[n_] := Floor[r*n]; (*A001951*)

%t v[n_] := Floor[(2 + r) n]; (*A001952*)

%t a[1] = 0; a[2] = 0; h = 200;

%t c = Table[u[n], {n, 1, h}];

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

%t Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}]; (*A189078*)

%t Table[a[c[[n]]] = a[n], {n, 1, h}] (*A189078*)

%t Flatten[Position[%, 0]] (*A189079*)

%t Flatten[Position[%%, 1]] (*A189080*)

%Y Cf. A188967, A189079, A189080, A189081.

%K nonn

%O 1

%A _Clark Kimberling_, Apr 16 2011