

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.


REFERENCES

Beeckmans, L. "The Splitting Algorithm for Egyptian Fractions." J. Number Th. 43, 173185, 1993.


LINKS

Hugo van der Sanden and others, Table of n, a(n) for n = 1..14
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. [From Robert G. Wilson v, Jun 10 2010]
Sequence in context: A226588 A005741 A033911 * A012916 A012921 A280468
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



