%I A006842 M0041
%S A006842 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,
%T A006842 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,
%U A006842 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
%N A006842 Numerators of Farey series of orders 1, 2, ....
%D A006842 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 
               1996, p. 152
%D A006842 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 23.
%D A006842 W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 
               2 vols., 1956, Vol. 1, p. 154.
%D A006842 I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers. 
               2nd ed., Wiley, NY, 1966, p. 141.
%D A006842 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006842 N. J. A. Sloane, <a href="stern_brocot.html">Stern-Brocot or Farey Tree</
               a>
%H A006842 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 A006842 <a href="Sindx_St.html#Stern">Index entries for sequences related to 
               Stern's sequences</a>
%e A006842 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 A006842 Farey := proc(n) sort(convert(`union`({0},{seq(seq(m/k,m=1..k),k=1..n)}),
               list)) end: seq(numer(Farey(i)),i=1..5); [From Peter Luschny (peter(AT)luschny.de), 
               Apr 28 2009]
%t A006842 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)
%Y A006842 Cf. A006843, A049455, A049456, A007305, A007306.
%Y A006842 Sequence in context: A024940 A054635 A003137 this_sequence A060505 A035188 
               A066295
%Y A006842 Adjacent sequences: A006839 A006840 A006841 this_sequence A006843 A006844 
               A006845
%K A006842 nonn,nice,frac,tabf
%O A006842 1,9
%A A006842 N. J. A. Sloane (njas(AT)research.att.com).
%E A006842 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 08 2004