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 A188967 Zero-one sequence based on (3n-2): a(A016777(k))=a(k); a(A007494(k))=1-a(k); a(1)=0. 45
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS 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: from triangular numbers: A189011 from squares: A188973 from pentagonal numbers: A189014 from hexagonal numbers: A189212 from Beatty [n*sqrt(2)]: A189078 and A189081 from cubes: A189008 from primes: A189141 from (3n): A189215 and A189222 from (3n-1): A189097 from (3n-2): A188967 from (4n): A189289, A189292, A189275, A189298 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 EXAMPLE 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. MATHEMATICA u[n_] := 3n - 2;  (*A016777*) 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*) PROG (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 ..]]) -- Reinhard Zumkeller, May 18 2015 CROSSREFS Cf. A188968, A188969. Cf. A257998 (partial sums), A258062 (run lengths). Sequence in context: A285830 A288741 A327183 * A090171 A316832 A188973 Adjacent sequences:  A188964 A188965 A188966 * A188968 A188969 A188970 KEYWORD nonn AUTHOR Clark Kimberling, Apr 14 2011 STATUS approved

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Last modified October 20 11:18 EDT 2019. Contains 328257 sequences. (Running on oeis4.)