id:A093873 - OEIS Search Results

Search: id:A093873

Displaying 1-1 of 1 results found.

page 1

Numerators in Kepler's tree of harmonic fractions.

+0
12

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, 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, 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 (list; graph; listen)

	OFFSET	`1,5`
	COMMENT	`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).` `a(A029744(n-1)) = 1; a(A070875(n-1)) = 2; a(A123760(n-1)) = 3. - Reinhard Zumkeller, Oct 13 2006`
	LINKS	`R. Zumkeller, Table of n, a(n) for n = 1..10000`
	FORMULA	`a(n) = a([n/2])(1 - n mod 2) + A093875([n/2])(n mod 2).`
	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`
	CROSSREFS	`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.` `Sequence in context: A112309 A160006 A060682 this_sequence A161148 A143773 A053279` `Adjacent sequences: A093870 A093871 A093872 this_sequence A093874 A093875 A093876`
	KEYWORD	`nonn,easy,frac`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com) and Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 24 2004`

page 1

Search completed in 0.002 seconds

Last modified November 29 12:46 EST 2009. Contains 167659 sequences.

AT&T Labs Research