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A188967
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Zero-one sequence based on (3n-2): a(A016777(k))=a(k); a(A007494(k))=1-a(k); a(1)=0.
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45
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0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0
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OFFSET
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1
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COMMENTS
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Compare with the generation of the Thue-Morse sequence T=A010060 from T(2n-1)=T(n), T(2n)=1-T(n), T(1)=0.
Other zero-one sequences generated in this manner:
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LINKS
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EXAMPLE
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Let u=A016777 and v=A007494, so that u(n)=3n-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).
a(2)=a(v(1))=1-a(1)=1
a(3)=a(v(2))=1-a(2)=0
a(4)=a(u(2))=a(2)=1.
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MATHEMATICA
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a[1] = 0; h = 128;
c = (u[#1] &) /@ Range[h];
d = (Complement[Range[Max[#1]], #1] &)[c]; (*A007494*)
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];
Table[a[c[[n]]] = a[n], {n, 1, h}] (*A188967*)
Flatten[Position[%, 0]] (*A188968*)
Flatten[Position[%%, 1]] (*A188969*)
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PROG
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(Haskell)
import Data.List (transpose)
a188967 n = a188967_list !! (n-1)
a188967_list = 0 : zipWith ($)
(cycle [(1 -) . a188967, (1 -) . a188967, a188967])
(concat $ transpose [[1, 3 ..], [2, 4 ..], [2 ..]])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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