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

Georgi Guninski guninski at guninski.com
Sun Oct 21 17:31:04 CEST 2012


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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