[seqfan] Re: Bounded egyptian fractions summing to 1

[Eric Angelini]

Hello Hugo,

> Given that it is not asserted to be a unique solution for that x, 
> or even minimal solution for that x

... Oh, I thought it was the lexicographically first such sum
for x = 1000, sorry.
Best,
É.



-----Message d'origine-----
De : SeqFan [mailto:seqfan-bounces at list.seqfan.eu] De la part de hv at crypt.org
Envoyé : jeudi 23 juillet 2015 14:26
À : Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Objet : [LIKELY_SPAM][seqfan] Re: Bounded egyptian fractions summing to 1

Eric Angelini <Eric.Angelini at kntv.be> wrote:
:Hello Seqfans,
:I think this finite seq should enter the OEIS.
:It is explained and visible here, on page 10 (on 65):
:http://www.math.ubc.ca/~gerg/slides/Urbana-27March09.pdf
:
:S = {97, 103, [.. snip ..] 999}

This is a particular example of a solution to the question "what sets of distinct unit fractions sum to 1, if we require each denominator to be <= x", for the particular value x = 1000.

Given that it is not asserted to be a unique solution for that x, or even minimal solution for that x, and given that there's nothing asserted to be especially notable about taking x = 1000, to me it doesn't seem general enough to include.

A sequence such as 'those x for which the smallest bounded set is greater than for x - 1' or 'the size of the smallest bounded set for x' seem more likely to be interesting (and may already be in); I guess they'd need a fair amount of computation though.

Hugo

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