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Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 910 2014.
The SternBrocot or Farey TreeThere are several versions of this tree. This one, which appears in R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. AddisonWesley, Reading, MA, 1990, p. 117, was drawn by Alexander Bogomolny. For another version see J. C. Lagarias, Number Theory and Dynamical Systems, pp. 3572 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 SternBrocot tree. There are also many associated sequences:
