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A006843
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Denominators of Farey series of orders 1, 2, ....
(Formerly M0081)
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14
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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; refs; listen; history; internal format)
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OFFSET
| 1,4
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REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
Alois P. Heinz, Table of n, a(n) for n = 1..10563
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EXAMPLE
| 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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MAPLE
| Farey := proc(n) sort(convert(`union`({0}, {seq(seq(m/k, m=1..k), k=1..n)}), list)) end: seq(denom(Farey(i)), i=1..5); [From Peter Luschny (peter(AT)luschny.de), Apr 28 2009]
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MATHEMATICA
| 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
| Cf. A006842, A049455, A049456, A007305, A007306. Also A177405/A177407.
Sequence in context: A132463 A153901 A132844 * A049456 A117506 A179205
Adjacent sequences: A006840 A006841 A006842 * A006844 A006845 A006846
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KEYWORD
| nonn,nice,frac,tabf
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 08 2004
Changed offset (=order of first row) to 1 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 26 2009
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