login
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
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}.
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
KEYWORD
nonn,tabf
AUTHOR
Reinhard Zumkeller, Jan 01 2009
STATUS
approved