[seqfan] Re: Prime production length of n

[Neil Sloane]

Maximilian, To all your variations, my answer is Yes, please include them
in the OEIS! This is an important subject, and worth including in several
ways in the OEIS.
Thanks!
Neil

On Sat, Mar 3, 2012 at 4:37 PM, Maximilian Hasler <
maximilian.hasler at gmail.com> wrote:

> On Fri, Mar 2, 2012 at 4:59 PM, Neil Sloane <njasloane at gmail.com> wrote:
> > http://m-hikari.com/ija/ija-2012/ija-1-4-2012/xushaojiIJA1-4-2012.pdf.
> > seems to suggest that there are two sequences that should be in the OEIS:
> > the prime production length of the polynomial x^2+x+n,
> > where n runs through the positive (or negative) integers.
>
> I started with
>
> https://oeis.org/A208936
> Prime production length of the polynomial P=x^2+x+prime(n): max { k>0
> | P(x) is prime for all x=0,...,k-1 }
>
> There are simple variations which essentially contain the same information:
> One could also consider P=x^2-x+n,
> which would yield zero for all composite numbers,
> unless one would start with x=1,2,3,...
>
> One could also consider Q=x^2 - x + n (or +prime(n)),
> again with x=0,... or x=1,...
> (This sign was Euler's choice).
> It amounts to increase all values by 1
> (since Q(x) = P(-x) = P(x-1).)
>
> Following the previous remark, allowing negative x
> also would not add more information.
>
> Would it be worth to add the "aeration" with prime(n) replaced by n,
> [not really aeration, esp. when the start x=0 is changed to x=1 in the "+"
> case]
> and/or the version(s) with switched sign where all (nonzero) values
> are augmented by 1 ?
>
> Maximilian
>



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