The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
Stern_Brocot.html

## The Stern-Brocot or Farey Tree

There are several versions of this tree. This one, which appears in R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 117, was drawn by Alexander Bogomolny. For another version see J. C. Lagarias, Number Theory and Dynamical Systems, pp. 35-72 of S. A. Burr, ed., The Unreasonable Effectiveness of Number Theory, Proc. Sympos. Appl. Math., 46 (1992). Amer. Math. Soc.

The nth order Farey series is the set of reduced fractions between 0 and 1 whose denominators are n or less, arranged in increasing order, and corresponds to a subtree of the Stern-Brocot tree.

There are also many associated sequences:

• The numerators and denominators of the fractions in the full tree give A007305/A047679.
• The numerators and denominators of the fractions in the left-hand subtree give A007305/A007306.
• The numerators and denominators of the triangle whose nth row consists of the Farey series of order n give A006842/A006843.