[seqfan] Re: A sequence and a related array

[Charles Greathouse]

Can't you just use that same trick, though? m(m+1)(m+2) + 3 is irreducible
and always divisible by 3, m(m+1)...(m+100) + 100 is always divisible by
100, and so on. Were you to hit a reducible polynomial you could just add
the target number again until you're irreducible again. So I think Sada
Numbers are just A000012. :)

On Sun, Jul 4, 2021 at 12:56 PM Ali Sada via SeqFan <seqfan at list.seqfan.eu>
wrote:

>  Thank you Olivier for your response. I really appreciate it.
> I strongly suggest that we change the name to "Sada Numbers". Just because
> Mr. Kempner was born 90 years before me doesn't give him the right to take
> my idea. :)
>
> Or, we can change the definition a little bit to "non-factorable
> polynomials". For example, a(2) = 1 because we get 2 from m^2+m+2, and that
> makes a(4) = 2. Would that be a unique and acceptable sequence?
> And what about the array? Was it another glorious wheel reinvention on my
> side?
>
> Best,
> Ali
>
>
>
>     On Sunday, July 4, 2021, 7:18:23 AM GMT, Olivier Gerard <
> olivier.gerard at gmail.com> wrote:
>
>  The sequence you are looking for is
> "Kempner Numbers", A002034
>
> 1, 2, 3, 4, 5, 3, 7, 4, 6, 5, 11, 4, 13, 7, 5, 6, 17, 6, 19, 5, 7, ...
>
> Olivier Gérard
>
>
> On Sun, Jul 4, 2021 at 10:15 AM Ali Sada via SeqFan <seqfan at list.seqfan.eu
> >
> wrote:
>
> > Hi everyone,
> >
> > If we want to make sure that we have a multiple of a certain positive
> > integer n we can simply multiply n consecutive integers. For example,
> > multiplying 11 consecutive numbers will certainly give us a multiple of
> 11.
> > However, some numbers don’t need n terms to get that multiple. For
> > example, we can get a multiple of 6 by multiplying only three integers
> > m(m+1)(m+2), which means that a(6) = 3. Or if we want a multiple of 7 we
> > need only five terms m(m+1) (m-1)(m^2+m+1)(m^2-m+1). So, what is the
> least
> > number of these non-factor-able terms we need to multiply in order to
> get a
> > multiple of n? I would really appreciate your help with this sequence if
> > you thought it’s suitable for the OEIS.
> >
> > The related array is “the largest common factor of m^k-m^n, where m > 1,
> n
> > = 1,2,3,.., and k > n."
> > For example, the largest common factor of m^8-m^2 is 252. I would
> > appreciate your help with this one too.
> >
> > Best,
> >
> > Ali
> >
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>