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A030300 Runs have lengths 2^n, n >= 0. 9
1, 0, 0, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

An example of a sequence with property that the fraction of 1's in the first n terms does not converge to a limit. - N. J. A. Sloane, Sep 24 2007

Image, under the coding sending a,d,e -> 1 and b,c -> 0, of the fixed point, starting with a, of the morphism a -> ab, b -> cd, c -> ee, d -> eb, e -> cc. - Jeffrey Shallit, May 14 2016

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

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

R. Stephan, Table of generating functions

R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences, arXiv:math/0307027 [math.CO], 2003.

Index entries for sequences related to binary expansion of n

Index entries for characteristic functions

FORMULA

a(n) = (1/2)*(1+(-1)^floor(log_2(n))). - Benoit Cloitre, Feb 22 2003

G.f.: 1/(1-x) * Sum_{k>=0} (-1)^k*x^2^k. - Ralf Stephan, Jul 12 2003

a(n) = 1 - a(floor(n/2)). - Vladeta Jovovic, Aug 04 2003

a(n) = A115253(2n, n) mod 2. - Paul Barry, Jan 18 2006

a(n) = 1 - A030301(n). - Antti Karttunen, Oct 10 2017

MAPLE

f0 := n->[seq(0, i=1..2^n)]; f1 := n->[seq(1, i=1..2^n)]; s := []; for i from 0 to 4 do s := [op(s), op(f1(2*i)), op(f0(2*i+1))]; od: A030300 := s;

MATHEMATICA

nMax = 6; Table[1 - Mod[n, 2], {n, 0, nMax}, {2^n}] // Flatten (* Jean-Fran├žois Alcover, Oct 20 2016 *)

CROSSREFS

Cf. A030301. Partial sums give A079947.

a(n) = A065359(n) + A083905(n).

Characteristic function of A053738.

Sequence in context: A071001 A072792 A116937 * A168394 A072770 A071674

Adjacent sequences:  A030297 A030298 A030299 * A030301 A030302 A030303

KEYWORD

nonn,base,easy

AUTHOR

Jean-Paul Delahaye (Jean-Paul.Delahaye(AT)lifl.fr)

STATUS

approved

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Last modified February 20 08:54 EST 2018. Contains 299384 sequences. (Running on oeis4.)