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A153778 Binary sequence constructed like a Stern-Brocot tree between 0 and 1, where XOR is applied instead of the mediant operation. 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, 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 20 11:28 EDT 2019. Contains 325180 sequences. (Running on oeis4.)