A153778 Binary sequence constructed like a Stern-Brocot tree between 0 and 1, where XOR is applied instead of the mediant operation.

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

Offset

1,1

Comments

The Jacobsthal sequence gives numbers of zeros and ones in the rows of the tree:

A001045(k) = #{i: 2^k <= i < 2^(k+1) and a(i)=0};

A001045(k+1) = #{i: 2^k <= i < 2^(k+1) and a(i)=1}.

Links

Table of n, a(n) for n=1..105.

N. J. A. Sloane, Stern-Brocot or Farey Tree

Index entries for sequences related to Stern's sequences

Formula

a(1) = 1 and for n>1: a(n) = if A025480(n-1)<>0 and A025480(n)<>0 then a(A025480(n-1)) XOR a(A025480(n)) else if A025480(n)=0 then 1-a(A025480(n-1)) else a(A025480(n-1)).

Example

.[0] . . . . . . . . . . . . . . . . . [1]
................... 1
........... 1 ............. 0
....... 1 ..... 0 ..... 1 ..... 1
..... 1 . 0 . 1 . 1 . 0 . 1 . 1 . 0
.... 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1.

Crossrefs

Sequence in context: A065535 A285518 A093719 * A065251 A039982 A267349

Adjacent sequences: A153775 A153776 A153777 * A153779 A153780 A153781

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Jan 01 2009

Status

approved