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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).
4

%I #4 Mar 30 2012 18:57:23

%S 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 52,54,55,57,58,59,61,64,68,69,73,75,76,77,81,83,84,86,87,88,91,92,93,

%U 95,98,102,103,107,109,110,111,115,117,118,120,121,122,124,128

%N 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 It is conjectured at A095076 that the zero-sequence s is A095076.

%t r=(1+5^(1/2))/2; u[n_] := Floor[n*r]; (*A000201*)

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

%t c = (u[#1] &) /@ Range[2h];

%t d = (Complement[Range[Max[#1]], #1] &)[c]; (*A001950*)

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

%t Table[a[c[[n]]] = a[n], {n, 1, h}] (*A095076 conjectured*)

%t Flatten[Position[%, 0]] (*A189034*)

%t Flatten[Position[%%, 1]] (*A189035*)

%Y A095076, A189035.

%K nonn

%O 1,2

%A _Clark Kimberling_, Apr 15 2011