

A130691


Number of distinct unit fractions required to sum to n when using the "splitting algorithm".


1




OFFSET

1,2


COMMENTS

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.


LINKS

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, 173185, 1993.
Hugo van der Sanden and others, Table of n, a(n) for n = 1..17 [Included as an "afile", since the last three terms exceed the limit for terms in bfiles.]


EXAMPLE

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.


CROSSREFS

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


KEYWORD

nonn,nice


AUTHOR

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


STATUS

approved



