Value a(6) in doubt for a =

[Maximilian Hasler]

> > (08:48) gp > sum(i=1,#a6,1/i)
>
> I think you meant 1/a6[i] not 1/i.

well, of course. (*shame on me....*)
I should really sleep a bit more...

Mea culpa....

M.H.



Rainer Rosenthal <r.rosenthal at web.de> wrote:
:The values of
:http://www.research.att.com/~njas/sequences/A101877
:are defined as  a(n) = max(S_n) where the sum of
:reciprocals of S_n is n. It is claimed that no S_n
:with smaller maximum could be found.
:
:I checked
:
:        ReciprocalSum(S_n) = n
:
:for n=1..6 and it was correct for n=1..5 but incorrect
:for n=6:
:
:    ReciprocalSum(S_6) is less than 6 (about 5.76).
:
:I wasn't able to guess what's wrong with S_6 but following
:a remark about the inclusion of S_n in S_{n+1} I checked
:whether S_5 was a subset of the S_6, given there. An no,
:it is not. S_6 lacks {80, 112, 144, 154, 165, 175, 176},
:but adding these is not enough.
:
:How to repair the description of A101877 and confirm
:a(6) = 469?

Bother. I agree S(6) as shown doesn't add up to 6.

Looking at the archive of the code I used for this, I assume I used
the last version to calculate a(6). I've made this available at
<http://crypt.org/hv/puzzle/A101877.pl-0.06> in case you want to take
a look. (Perl code with inline C, requires the Inline module from CPAN.)

Trying to run this with the recently released perl-5.10.0 gives me an
immediate SEGV (which I'll investigate separately).

Running it on perl-5.8.8, it successfully prints the following:
a(6) = 469 : {
}

.. which I believe is the correct set. The missing numbers were:

I have no idea why I posted the wrong set before, but maybe this is a good
time to see if I can determine a(7) now, and there is the chance I would
discover that along the way.

Apologies for the inconvenience, and thanks for spotting the error.

Hugo