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).

1, 5, 7, 8, 10, 11, 12, 15, 16, 17, 19, 23, 24, 25, 27, 30, 34, 36, 37, 38, 40, 43, 47, 48, 52, 54, 55, 57, 58, 59, 61, 64, 68, 69, 73, 75, 76, 77, 81, 83, 84, 86, 87, 88, 91, 92, 93, 95, 98, 102, 103, 107, 109, 110, 111, 115, 117, 118, 120, 121, 122, 124, 128

Offset: 1

Author

Clark Kimberling, Apr 15 2011

Keywords

• nonn

Comments

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

Crossrefs

A095076, A189035.

Programs

Mathematica

r=(1+5^(1/2))/2; u[n_] := Floor[n*r];  (*A000201*)
a[1] = 0; h = 128;
c = (u[#1] &) /@ Range[2h];
d = (Complement[Range[Max[#1]], #1] &)[c]; (*A001950*)
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];
Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A095076 conjectured*)
Flatten[Position[%, 0]]  (*A189034*)
Flatten[Position[%%, 1]] (*A189035*)