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3 unusual facts about Farey sequence


Equivalent impedance transforms

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.

Farey sequence

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).

Farey sequences are named after the British geologist John Farey, Sr., whose letter about these sequences was published in the Philosophical Magazine in 1816.



see also