The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A093875 Denominators in Kepler's tree of harmonic fractions. 8
 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, 6, 6, 9, 9, 10, 10, 11, 11, 9, 9, 12, 12, 11, 11, 13, 13, 6, 6, 9, 9, 10, 10, 11, 11, 9, 9, 12, 12, 11, 11, 13, 13, 7, 7, 11, 11, 13, 13, 14, 14, 13, 13, 17, 17, 15, 15, 18, 18, 11, 11, 16, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). It appears that A071585 is a bisection of this sequence, which itself is a bisection of A093873. - Yosu Yurramendi, Jan 09 2016 LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = a([n/2]) + A093873([n/2]). Conjecture of the comment in detail: a(2n+1) = a(2n), n > 0;  a(2n+1) = A071585(n), n >= 0; a(2n) = A071585(n), n > 0. - Yosu Yurramendi, Jun 22 2016 a(2n) - A093873(2n) = a(n), n > 0; a(2n+1) - A093873(2n+1) = A093873(n), n > 0. - Yosu Yurramendi, Jul 23 2016 From Yosu Yurramendi, Jul 25 2016: (Start) a(2^m)  = m+1, m >= 0; a(2^m + 2) = 2m - 1, m >= 1; a(2^m - 1) = A000045(m+2), m >= 1. a(2^(m+1) + k) - a(2^m + k) = a(k),   m > 0, 0 <= k < 2^m. For k=0, a(0) = 1 is needed. a(2^(m+2) - k - 1) = a(2^(m+1) - k - 1) + a(2^m - k - 1), m >= 0, 0 <= k < 2^m. (End) EXAMPLE The first few fractions are: 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 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 MATHEMATICA num = num = 1; den = 1; den = 2; num[n_?EvenQ] := num[n] = num[n/2]; den[n_?EvenQ] := den[n] = num[n/2] + den[n/2]; num[n_?OddQ] := num[n] = den[(n-1)/2]; den[n_?OddQ] := den[n] = num[(n-1)/2] + den[(n-1)/2]; A093875 = Table[den[n], {n, 1, 83}] (* Jean-François Alcover, Dec 16 2011 *) CROSSREFS The numerators are in A093873. 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. Cf. A071585, A093873 Sequence in context: A116458 A354166 A331854 * A329242 A266193 A114214 Adjacent sequences:  A093872 A093873 A093874 * A093876 A093877 A093878 KEYWORD nonn,easy,frac AUTHOR N. J. A. Sloane and Reinhard Zumkeller, May 24 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 1 13:12 EDT 2022. Contains 354973 sequences. (Running on oeis4.)