Search: id:A093873
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%I A093873
%S A093873 1,1,1,1,2,1,2,1,3,2,3,1,3,2,3,1,4,3,4,2,5,3,5,1,4,3,4,2,5,3,5,1,5,4,5,
%T A093873 3,7,4,7,2,7,5,7,3,8,5,8,1,5,4,5,3,7,4,7,2,7,5,7,3,8,5,8,1,6,5,6,4,9,5,
%U A093873 9,3,10,7,10,4,11,7,11,2,9,7,9,5,12,7,12,3,11,8,11,5,13,8,13,1,6
%N A093873 Numerators in Kepler's tree of harmonic fractions.
%C A093873 Form a tree of fractions by beginning with 1/1 and then giving every 
               node i/j two descendants labeled i/(i+j) and j/(i+j).
%C A093873 a(A029744(n-1)) = 1; a(A070875(n-1)) = 2; a(A123760(n-1)) = 3. - Reinhard 
               Zumkeller, Oct 13 2006
%H A093873 R. Zumkeller, <a href="b093873.txt">Table of n, a(n) for n = 1..10000</
               a>
%F A093873 a(n) = a([n/2])*(1 - n mod 2) + A093875([n/2])*(n mod 2).
%e A093873 The first few fractions are:
%e A093873 1 1 1 1 2 1 2 1 3 2 3 1 3 2 3 1 4 3 4 2 5 3 5 1 4 3 4 2 5 3 5
%e A093873 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ...
%e A093873 1 2 2 3 3 3 3 4 4 5 5 4 4 5 5 5 5 7 7 7 7 8 8 5 5 7 7 7 7 8 8
%Y A093873 The denominators are in A093875. Usually one only considers the left-hand 
               half of the tree, which gives the fractions A020651/A086592. See 
               A086592 for more information, references to Kepler, etc.
%Y A093873 Sequence in context: A112309 A160006 A060682 this_sequence A161148 A143773 
               A053279
%Y A093873 Adjacent sequences: A093870 A093871 A093872 this_sequence A093874 A093875 
               A093876
%K A093873 nonn,easy,frac
%O A093873 1,5
%A A093873 N. J. A. Sloane (njas(AT)research.att.com) and Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 24 2004

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