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Search: id:A006842
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| A006842 |
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Numerators of Farey series of orders 1, 2, ....
(Formerly M0041)
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+0
9
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| 0, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 2, 3, 1, 0, 1, 1, 1, 2, 1, 3, 2, 3, 4, 1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 3, 4, 5, 1, 0, 1, 1, 1, 1, 2, 1, 2, 3, 1, 4, 3, 2, 5, 3, 4, 5, 6, 1, 0, 1, 1, 1, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 5, 6, 7, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 4, 1, 5, 4, 3, 5, 2, 5
(list; graph; listen)
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OFFSET
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1,9
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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[ Numerator[ Farey[n]], {n, 0, 9}]] (from Robert G. Wilson v Apr 08 2004)
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CROSSREFS
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Cf. A006843, A049455, A049456, A007305, A007306.
Sequence in context: A024940 A054635 A003137 this_sequence A060505 A035188 A066295
Adjacent sequences: A006839 A006840 A006841 this_sequence A006843 A006844 A006845
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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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