[seqfan] Re: Bounded egyptian fractions summing to 1

hv at crypt.org hv at crypt.org
Thu Jul 23 14:25:37 CEST 2015

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):
: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.


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