A188967 - OEIS

A188967

Zero-one sequence based on (3n-2): a(A016777(k))=a(k); a(A007494(k))=1-a(k); a(1)=0.

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

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*)