# [seqfan] Re: Bounded egyptian fractions summing to 1

Benoît Jubin benoit.jubin at gmail.com
Thu Jul 23 23:38:29 CEST 2015

```The slides you mention study the asymptotic behaviour of the sequence of
integers that are not the largest denominator in an Egyptian fraction
summing to 1, which seems to be the complement of A092671, but might
deserve its own entry with a link to Greg Martin's slides and papers.

On Thu, Jul 23, 2015 at 5:08 PM, Eric Angelini <Eric.Angelini at kntv.be>
wrote:

> 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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```