id:A093875 - OEIS Search Results

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Denominators in Kepler's tree of harmonic fractions.

+0
6

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; listen)

	OFFSET	`1,2`
	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).`
	LINKS	`R. Zumkeller, Table of n, a(n) for n = 1..10000`
	FORMULA	`a(n) = a([n/2]) + A093873([n/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 numerators 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: A101402 A156251 A116458 this_sequence A114214 A074198 A048688` `Adjacent sequences: A093872 A093873 A093874 this_sequence A093876 A093877 A093878`
	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`

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Last modified November 25 13:47 EST 2009. Contains 167481 sequences.

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