%I A086592
%S A086592 2,3,3,4,4,5,5,5,5,7,7,7,7,8,8,6,6,9,9,10,10,11,11,9,9,12,12,11,11,13,
%T A086592 13,7,7,11,11,13,13,14,14,13,13,17,17,15,15,18,18,11,11,16,16,17,17,19,
%U A086592 19,14,14,19,19,18,18,21,21,8,8,13,13,16,16,17,17,17,17,22,22,19,19,23
%N A086592 Denominators in left-hand half of Kepler's tree of fractions.
%C A086592 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 A086592 Level n of the tree consists of 2^n nodes: 1/2; 1/3, 2/3; 1/4, 3/4, 2/
               5, 3/5; 1/5, 4/5, 3/7, 4/7, 2/7, 5/7, 3/8, 5/8; ...
%D A086592 Johannes Kepler, Mysterium cosmographicum, Tuebingen, 1596, 1621, Caput 
               XII.
%D A086592 Johannes Kepler, Harmonice Mundi, Linz, 1619, Liber III, Caput II.
%D A086592 Johannes Kepler, The Harmony of the World [1619], trans. E. J. Aiton, 
               A. M. Duncan and J. V. Field, American Philosophical Society, Philadelphia, 
               1997, p. 163.
%H A086592 Johannes Kepler, <a href="http://www.iki.fi/~kartturi/Kepler/a086592.htm">
               Excerpt from the Chapter II of the Book III of the Harmony of the 
               World: On the seven harmonic divisions of the string</a> (illustrates 
               the A020651/A086592-tree).
%Y A086592 Bisection of A020650.
%Y A086592 See A093873/A093875 for the full tree.
%Y A086592 a(n) = A020650(n)+A020651(n) = A020650(2n). A020651 gives the numerators. 
               Bisection: A086593. Cf. A002487, A004169.
%Y A086592 Sequence in context: A038567 A036234 A061091 this_sequence A132663 A023964 
               A000267
%Y A086592 Adjacent sequences: A086589 A086590 A086591 this_sequence A086593 A086594 
               A086595
%K A086592 nonn,frac,tabf
%O A086592 1,1
%A A086592 Antti Karttunen (his_firstname.his_surname(AT)iki.fi) Aug 28 2003
%E A086592 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), May 24 2004