[seqfan] Re: Pieces of cake sequence A265286 and a question

Max Alekseyev maxale at gmail.com
Fri Jan 22 22:34:00 CET 2016


Neil,
I'm sorry I misread your question. I do not know the answer and believe
your question is a hard one, provided that we don't even know how to
compute A265286 efficiently.
Regards,
Max

On Fri, Jan 22, 2016 at 4:31 PM, Max Alekseyev <maxale at gmail.com> wrote:

> Hi Neil,
> The second example in A265286 negatively answers your question.
> Regards,
> Max
>
> On Fri, Jan 22, 2016 at 3:45 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
>> Rainer R. mentioned Max Alekseyev's lovely sequence A265286.
>>
>> Given n, look for the smallest set of fractions {f_1, f_2, ..., f_M} in
>> the
>> range 0 to 1 such that for each k with 1 <= k <= n, we can partition the
>> f_i into k groups whose sums are equal. For n=5 the minimal M is 9, and a
>> solution is
>> {1/60, 1/30, 1/20, 1/12, 7/60, 2/15, 1/6, 1/5, 1/5}
>>
>> OK, now look at all the solutions for a given value of n,
>> with M (the minimal value) parts. Now ask, what is the minimal
>> denominator?
>>
>> Is it always A003418(n) = LCM{1,2,...,n}?
>>
>> If not, we get a new sequence: given n, first minimize the number of
>> parts,
>> then minimize the biggest denominator
>>
>> Max, do you know the answer?
>>
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>>
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>>
>
>


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