%I
%S 0,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,1,1,0,0,1,0,0,1,
%T 0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,1,1,0,
%U 0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0
%N Zeroone sequence based on the sequence floor(n*sqrt(2)): a(A001951(k))=a(k); a(A001952(k))=1a(k); a(1)=0, a(2)=1.
%e Let u=A001951=(Beatty sequence for sqrt(2)) and v=A001952=(Beatty sequence for 2+sqrt(2)). Then A189081 is the sequence a given by a(u(k))=a(k); a(v(k))=1a(k), where a(0)=0 and a(1)=1.
%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] = 1; 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}]; (*A189081*)
%t Table[a[c[[n]]] = a[n], {n, 1, h}] (*A189081*)
%t Flatten[Position[%, 0]] (*A189082*)
%t Flatten[Position[%%, 1]] (*A189083*)
%Y Cf. A189078, A189082, A189083, A188967.
%K nonn
%O 1
%A _Clark Kimberling_, Apr 16 2011
