%C A136296 "Special augmented numbers" from Zak Seidov

[Maximilian Hasler]

Ooops... sorry for flooding the list, but I copy-pasted the wrong
lines, which yields some irreproducible results... Here's the
reproducible version:

A136296d(k)={ local( d=factor(10^(k+1)+1)[,1] );
 if( #d==1 | d[#d]<10^(k-1),[],vecextract( d, if(
d[#d-1]>10^(k-1),"-2..-1","-1"))~)}

for( k=1,99, print1(A136296d(k)))
[][11,13][137][9091][][909091][5882353][][][][][][][][][][][909090909090909091][][][][][][][][][][][]
[909090909090909090909090909091][][][][][][][][][][][][][][][][][][][][][]
[9090909090909090909090909090909090909090909090909091][][][][][][][][][][][][][]
[909090909090909090909090909090909090909090909090909090909090909091][][][][][]
*** factor: user interrupt

Sorry again for confusion.
M.H.

On Wed, Apr 23, 2008 at 5:24 PM, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:
> As I said in reply to Frank's mail yesterday morning, divisors()
>  should be replaced by factor()[,1], i.e.,
>  to get these primes with d digits, use:
>
>  A136296d(k) = { local( d = factor(10^(k+1)+1)[,1] );
>   if( d[#d]<10^(k-1), [], vecextract( d, if( d[#d-1]>10^(k-1),"-2..-1","-1"))~)
>
>  then:
>  for( k=1,99, print1(A136296d(k)))
>  [13][137][9091][][909091][5882353][][][][][][][][][][][909090909090909091][][][][][][][][][][][]
>  [909090909090909090909090909091][][][][][][][][][][][][][][][][][][][][][]
>  [9090909090909090909090909090909090909090909090909091][][][][][][][][][][][][][]
>  [909090909090909090909090909090909090909090909090909090909090909091][][][][]
>
>  PS: Oh, I just get Frank's reply with roughly the same code... well, a
>  bit different: it doesn't use the result that only the highest or
>  second highest divisor can be of needed length.
>



Artur:

Another reason I am cautious about these
things is that I do not have time
to check proofs!

So let me ask you: are you familiar with the
theory of quadratic forms?  
The classic work is:

D. Cox, Primes of the form x^2+ny^2, Wiley, 1989.

This gives a standard mechanism for proving or disproving

Neil