Title A107006

[Artur]

My sugestion was follow A007521 
<http://www.research.att.com/%7Enjas/sequences/A007521>
Also we can change title on   " Primes of the form 4x^2-4xy+5y^2 with x 
and y nonnegative."
Best wishes
Artur


Maximilian Hasler pisze:
> What one can say is e.g.
>
> %C A107006
> Identical to the list of primes = 7 (mod 24) at least for all 9824
> terms not exceeding 10^6.
> Since 4x^2-4xy+7y^2 = (2x-y)^2+6y^2 (x,y >= 0) can be prime only for
> odd y, the set can also be written as
> { primes of the form (2k+1)^2+6(2m+1)^2 ; k,m>=0 }.
> %H A107006 M. F. Hasler, <a
> href="http://www.research.att.com/~njas/sequences/b107006.txt">
>    Table of n, a(n) for n=1,...,9824</a>.
> %o A107006 (PARI)
> A107006(Nmax) = { local(S=[],t); forstep(y=1,sqrtint(Nmax\6),2,
> t=6*y^2; forstep(xx=1,sqrtint(Nmax-t),2, isprime(t+xx^2)|next;
> S=setunion(S,[t+xx^2]))); vecsort(eval(S)) }
> %o A107006 /* create list up to 10^6 */ A107006(10^6);
> %o A107006 /* check equality with primes = 7 mod 24 */
> c=0;p=1;while(c<#%,while((p=nextprime(p+1))% 24-7,); p==%[c++] & next;
> error([c,%[c],p]))
>
> Maximilian
>
>
> On Wed, Apr 23, 2008 at 10:22 AM, N. J. A. Sloane <njas at research.att.com> wrote:
>   
>> Artur,  Thanks for this comment.  Let me explain what I did and why.
>>  Subject: Re: Title A107006
>>  Cc: njas at research.att.com
>>
>>  I KNOW the definition is  Primes of the form 4x^2-4xy+7y^2, with x and y nonnegative
>>
>>  You tell me this is the same as  Primes of the form 24n+7.
>>
>>  But do you have a proof?  This subject is very tricky, as you know.
>>  Have you studied the book by Cox ?
>>
>>  I am not CERTAIN you have a proof that they are the same,
>>  so to be cautious I give your definition as a comment,
>>  with your name attached, in case it is wrong!
>>  In this case you may well have a proof, of course - do you?
>>
>>  >From: Artur <grafix at csl.pl>
>>  >Reply-To: grafix at csl.pl
>>  >To: seqfan <seqfan at ext.jussieu.fr>, noe at sspectra.com
>>  >Subject: Title A107006
>>
>>  >In my private opinion the title of A107006
>>  ><http://www.research.att.com/%7Enjas/sequences/A107006> would be better
>>  >if it was changed to the simpler version: "Primes of the form 24k+7"
>>  >Artur
>>     
>
>
>
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