[seqfan] Re: Integer sequence question at MathOverflow
Max Alekseyev
maxale at gmail.com
Tue May 22 15:28:53 CEST 2012
I asked Suzuki about sequence A020473 and he explained his approach:
He basically tracked all fractions <=1 that can be obtained by summing
up reciprocals of integers <= m. Growing m from 1 to n, he used a sort
of dynamic programming to compute the number of ways each fraction can
be obtained. At the end he gets the number of ways to represent 1 (as
well as any other smaller fraction) as the sum of reciprocals of
integers <= n.
He said that storing the dynamic programming table takes only about 12
GB for n=390; however for n=391 it would take about 450 GB.
This approach suggests the following sequence:
a(n) is the number of distinct fractions <=1 that can be obtained by
summing up reciprocals of integers <= n. (Basically it is the size of
dynamic programming table in Suzuki's approach).
Is it present in the OEIS? If not, could somebody please compute and submit it?
Regards,
Max
On Tue, May 8, 2012 at 6:13 PM, Olivier Gerard <olivier.gerard at gmail.com> wrote:
> I wonder as well.
>
> Suzuki Toshitaka computed lists for A092669 and A092671 and a few others.
>
> He can be reached at suzuki at scio.co.jp
>
> Olivier
>
>
> On Tue, May 8, 2012 at 2:08 AM, Max Alekseyev <maxale at gmail.com> wrote:
>
>> A020473
>
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