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

Emmanuel Vantieghem emmanuelvantieghem at gmail.com
Sun Oct 21 15:23:19 CEST 2012


I made a small table of the smallest value of  d(n)  such that  p(n)
splits completely in  Q[sqrt[d]]  and I found (from  n = 2 on) :
   d(n) = 7,6,2,3,3,2,5,2,5,2,3,2,6,2,6,3,3,6,...
(the value  d(n)  is the least  d  such that the quadratic character of the
field  Q(sqrt(d))  takes the value 1  at  p(n) ; the definition of
quadratic character comes from the book "Number Theory" of Borevich and
Shafarevich).
This seems not to match  A060084.  Where is my error ?
____________________________________________________
2012/10/21 Alonso Del Arte <alonso.delarte at gmail.com>

> 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
>
> --
> Alonso del Arte
> Author at SmashWords.com<
> https://www.smashwords.com/profile/view/AlonsoDelarte>
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>
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