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A130691
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Number of distinct unit fractions required to sum to n when using the "splitting algorithm".
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1
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OFFSET
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1,2
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COMMENTS
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The splitting algorithm decomposes a rational p/q to distinct unit fractions by first creating the multiset with p copies of 1/q, then repeatedly replacing a duplicated element 1/q' with the pair 1/(q'+1), 1/q'(q'+1) until no duplicates remain.
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LINKS
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Hugo van der Sanden and others, Table of n, a(n) for n = 1..14
L. Beeckmans, The Splitting Algorithm for Egyptian Fractions, J. Number Th. 43, 173-185, 1993.
Hugo van der Sanden and others, Table of n, a(n) for n = 1..17 [Included as an "a-file", since the last three terms exceed the limit for terms in b-files.]
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EXAMPLE
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For n=2, the algorithm generates the multisets {1/1, 1/1}, {1/1, 1/2, 1/2}, {1/1, 1/2, 1/3, 1/6}. The final multiset has no duplicate elements, so the algorithm terminates, and has 4 elements, so a(2)=4.
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CROSSREFS
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Cf. A002966. - Robert G. Wilson v, Jun 10 2010
Sequence in context: A318641 A005741 A033911 * A308239 A012916 A012921
Adjacent sequences: A130688 A130689 A130690 * A130692 A130693 A130694
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KEYWORD
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nonn,nice
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AUTHOR
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Hugo van der Sanden, Jun 10 2010, with contributions from Franklin T. Adams-Watters and Robert Gerbicz
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STATUS
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approved
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