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%I #8 Mar 30 2012 18:57:23
%S 0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,
%T 1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,
%U 0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0
%N Zero-one sequence based on squares: a(A000290(k))=a(k); a(A000037(k))=1-a(k); a(1)=0.
%C Let u=A000290 and v=A000037, so that u(n)=n^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).
%t u[n_] := n^2; (*A000290*)
%t a[1] = 0; h = 128;
%t c = (u[#1] &) /@ Range[h];
%t d = (Complement[Range[Max[#1]], #1] &)[c]; (*A000037*)
%t Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];
%t Table[a[c[[n]]] = a[n], {n, 1, h}] (*A188973*)
%t Flatten[Position[%, 0]] (*A188974*)
%t Flatten[Position[%%, 1]] (*A188975*)
%Y Cf. A188967, A188974, A188975.
%K nonn
%O 1
%A _Clark Kimberling_, Apr 14 2011
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