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Search: id:A006843
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| A006843 |
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Denominators of Farey series of orders 1, 2, ....
(Formerly M0081)
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+0
9
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| 1, 1, 1, 2, 1, 1, 3, 2, 3, 1, 1, 4, 3, 2, 3, 4, 1, 1, 5, 4, 3, 5, 2, 5, 3, 4, 5, 1, 1, 6, 5, 4, 3, 5, 2, 5, 3, 4, 5, 6, 1, 1, 7, 6, 5, 4, 7, 3, 5, 7, 2, 7, 5, 3, 7, 4, 5, 6, 7, 1, 1, 8, 7, 6, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 6, 7, 8, 1, 1, 9, 8, 7, 6, 5, 9, 4, 7, 3, 8, 5, 7, 9, 2, 9, 7, 5, 8, 3, 7
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 152
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 23.
W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 2 vols., 1956, Vol. 1, p. 154.
I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers. 2nd ed., Wiley, NY, 1966, p. 141.
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LINKS
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N. J. A. Sloane, Stern-Brocot or Farey Tree
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Stern's sequences
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EXAMPLE
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0/1, 1/1; 0/1, 1/2, 1/1; 0/1, 1/3, 1/2, 2/3, 1/1; 0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1; 0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1; ... = A006842/A006843
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MATHEMATICA
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Farey[n_] := Union[ Flatten[ Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; Flatten[ Table[ Denominator[ Farey[n]], {n, 0, 9}]] (from Robert G. Wilson v Apr 08 2004)
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CROSSREFS
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Cf. A006842, A049455, A049456, A007305, A007306.
Sequence in context: A104467 A132463 A132844 this_sequence A049456 A117506 A055089
Adjacent sequences: A006840 A006841 A006842 this_sequence A006844 A006845 A006846
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KEYWORD
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nonn,nice,frac,tabf
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AUTHOR
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njas
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 08 2004
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