A130691 Number of distinct unit fractions required to sum to n when using the "splitting algorithm".

1, 4, 16, 172, 4331, 232388, 4865293065, 40149851165417480, 18146043304242768613568943751063, 5522398183372890742378015411585945396419106762128927

Offset: 1

Author

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

Keywords

• nonn
• nice

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.

Examples

			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.
		

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, 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.]

Crossrefs

Cf. A002966. - Robert G. Wilson v, Jun 10 2010