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

[Max Alekseyev]

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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