For large n the size of the set has been found by numerical techniques to be approximately 2.53n and analytically strict bounds are given by a Farey sequence of Fibonacci numbers.
Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete Mathematics: A Foundation for Computer Science, 2nd Edition (Addison-Wesley, Boston, 1989); in particular, Sec. 4.5 (pp. 115–123), Bonus Problem 4.61 (pp. 150, 523–524), Sec. 4.9 (pp. 133–139), Sec. 9.3, Problem 9.3.6 (pp. 462–463).
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Farey sequences are named after the British geologist John Farey, Sr., whose letter about these sequences was published in the Philosophical Magazine in 1816.
sequence | Limit of a sequence | Thue–Morse sequence | sequence (poetry) | main sequence | John Farey, Sr. | Frölicher spectral sequence | Specker sequence | Sobol sequence | Shine-Dalgarno sequence | Sequence of Saint Eulalia | Sequence motif | Nucleic acid sequence | dream sequence | Xeelee Sequence | The Echorium Sequence | The Dark Is Rising Sequence | Slab monolith, like the first sequence of ''2001: A Space Odyssey | Signal sequence | Sequence (poetry) | Sequence (music) | Sequence learning | Sequence assembly | Regulatory sequence | regulatory sequence | Regular sequence (algebra) | Regular sequence | Rapid sequence induction | Novel sequence | Mid-May 2008 tornado outbreak sequence |