Search: id:A006843
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%I A006843 M0081
%S A006843 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,
%T A006843 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,
%U A006843 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
%N A006843 Denominators of Farey series of orders 1, 2, ....
%D A006843 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 
               1996, p. 152
%D A006843 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 23.
%D A006843 W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 
               2 vols., 1956, Vol. 1, p. 154.
%D A006843 I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers. 
               2nd ed., Wiley, NY, 1966, p. 141.
%D A006843 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006843 N. J. A. Sloane, <a href="stern_brocot.html">Stern-Brocot or Farey Tree</
               a>
%H A006843 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FareySequence.html">Link to a section of The World of Mathematics.</
               a>
%H A006843 <a href="Sindx_St.html#Stern">Index entries for sequences related to 
               Stern's sequences</a>
%e A006843 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
%p A006843 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]
%t A006843 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)
%Y A006843 Cf. A006842, A049455, A049456, A007305, A007306.
%Y A006843 Sequence in context: A132463 A153901 A132844 this_sequence A049456 A117506 
               A055089
%Y A006843 Adjacent sequences: A006840 A006841 A006842 this_sequence A006844 A006845 
               A006846
%K A006843 nonn,nice,frac,tabf
%O A006843 1,4
%A A006843 N. J. A. Sloane (njas(AT)research.att.com).
%E A006843 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 08 2004
%E A006843 Changed offset (=order of first row) to 1 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Apr 26 2009

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