[seqfan] Re: A sequence and a related array

[Ali Sada]

 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
>
>
>
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