A086694 A run of 2^n 1's followed by a run of 2^n 0's, for n=0, 1, 2, ...

1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0

Offset

1,1

Comments

First differences of A006165 and, likely, of A078881.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Ralf Stephan, Some divide-and-conquer sequences ...

Ralf Stephan, Table of generating functions

Formula

a(n) = 1-A079944(n-1) = 2-A079882(n-1) = A080791(n+1)-A083661(n+1).

a(n) = 1 - floor(log_2(4*(n+1)/3)) + floor(log_2(n+1)).

a(1) = 1, a(2) = 0, a(2n+1) = a(n), a(2n) = a(n-1).

G.f.: Sum_{k>=1} (x^(2^k)-x^(3*2^(k-1)))/(x-x^2). - Robert Israel, Jul 27 2017

G.f.: g(x) = (1/(1 - x))*( Sum_{n >= 1} x^(2^n-1)*(1 - x^2^(n-1)) ). Functional equation: g(x) = x + x*(1+x)*g(x^2). - Wolfgang Hintze, Aug 05 2017

Maple

seq(op([1$(2^n), 0$(2^n)]), n=0..6); # Robert Israel, Jul 27 2017

Mathematica

Table[{PadRight[{}, 2^n, 1], PadRight[{}, 2^n, 0]}, {n, 0, 5}]//Flatten (* Harvey P. Dale, May 29 2017 *)
Table[{Array[1&, 2^n], Array[0&, 2^n]}, {n, 0, 5}]//Flatten (* Wolfgang Hintze, Jul 27 2017 *)

Prog

(PARI) a(n)=if(n<3, if(n<2, 1, 0), if(n%2==0, a(n/2-1), a((n-1)/2)))

Crossrefs

Cf. A005942, A079944.

Sequence in context: A179762 A263804 A120526 * A357518 A093317 A127253

Adjacent sequences: A086691 A086692 A086693 * A086695 A086696 A086697

Keyword

nonn,easy

Author

Ralf Stephan, Sep 12 2003

Status

approved