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

Author

Reinhard Zumkeller, Jan 01 2009

Keywords

• nonn
• tabf

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}.

Examples

			.[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.
		

Links

• 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)).