[seqfan] Re: Is A060084 the answer to this question?

[Neil Sloane]

I hope you will add those missing sequences to the OEIS!

Neil

On Sun, Oct 21, 2012 at 11:31 AM, Georgi Guninski <guninski at guninski.com>wrote:

> On Sat, Oct 20, 2012 at 07:46:30PM -0400, Alonso Del Arte wrote:
> > Given the n-th prime p(n) in *Z*, what is the smallest positive
> > discriminant d such that p(n) is composite in *Z*[sqrt(d)]? I figured a
> few
> > terms and searched it, obtaining a handful or results. Of these, A060084
> > seems likeliest to be the right one. Is there a well-known result that
> > tells us that the least prime not a primitive root of p(n) is also the
> > smallest discriminant for a real field where p(n) is composite?
> >
> > Al
> >
>
> If I work over Q[sqrt(d)] get:
> A053760 Smallest positive quadratic nonresidue modulo p, where p is the
> n-th prime.
> and its duplicate A091382.
>
> Using sage and factoring over Z[sqrt(d)] (which translates to
> ZZ[sqrt(3)] == Order in Number Field in sqrt3 with defining
> polynomial x^2 - 3) don't get anything in OEIS.
>
> Q[sqrt(-d)] doesn't appear in OEIS too.
>
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-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
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