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A130691 Number of distinct unit fractions required to sum to n when using the "splitting algorithm". 1
1, 4, 16, 172, 4331, 232388, 4865293065, 40149851165417480, 18146043304242768613568943751063, 5522398183372890742378015411585945396419106762128927 (list; graph; refs; listen; history; text; internal format)



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.


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.]


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.


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




Hugo van der Sanden, Jun 10 2010, with contributions from Franklin T. Adams-Watters and Robert Gerbicz



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Last modified March 22 08:43 EDT 2023. Contains 361419 sequences. (Running on oeis4.)