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A189034 Positions of 0 in the zero-one sequence s based on the sequence lower Wythoff sequence p: s(p(k))=s(k); s(q(k))=1-s(k); s(1)=0, q=(upper Wythoff sequence).

%I A189034 #4 Mar 30 2012 18:57:23
%S A189034 1,5,7,8,10,11,12,15,16,17,19,23,24,25,27,30,34,36,37,38,40,43,47,48,
%T A189034 52,54,55,57,58,59,61,64,68,69,73,75,76,77,81,83,84,86,87,88,91,92,93,
%U A189034 95,98,102,103,107,109,110,111,115,117,118,120,121,122,124,128
%N A189034 Positions of 0 in the zero-one sequence s based on the sequence lower Wythoff sequence p:  s(p(k))=s(k); s(q(k))=1-s(k); s(1)=0, q=(upper Wythoff sequence).
%C A189034 It is conjectured at A095076 that the zero-sequence s is A095076.
%t A189034 r=(1+5^(1/2))/2; u[n_] := Floor[n*r];  (*A000201*)
%t A189034 a[1] = 0; h = 128;
%t A189034 c = (u[#1] &) /@ Range[2h];
%t A189034 d = (Complement[Range[Max[#1]], #1] &)[c]; (*A001950*)
%t A189034 Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];
%t A189034 Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A095076 conjectured*)
%t A189034 Flatten[Position[%, 0]]  (*A189034*)
%t A189034 Flatten[Position[%%, 1]] (*A189035*)
%Y A189034 A095076, A189035.
%K A189034 nonn
%O A189034 1,2
%A A189034 _Clark Kimberling_, Apr 15 2011