# [seqfan] Re: n-Wall-Sun-Sun primes

Max Alekseyev maxale at gmail.com
Thu Apr 21 22:59:29 CEST 2016

```Also, primes p=2 and p dividing k^2+4 should be excluded from consideration.
In fact, a k-Wall-Sun-Sun prime is the same as a Wall–Sun–Sun prime with
discriminant k^2+4 (as defined in Wikipedia).
Therefore, initial terms for smallest k-Wall-Sun-Sun primes can be
extracted from the table in Wikipedia for discriminants 2^2+4=8 (smallest
prime 13), 3^2+4=13 (smallest prime 241), etc.

Regards,
Max

On Thu, Apr 21, 2016 at 4:30 PM, Max Alekseyev <maxale at gmail.com> wrote:

> There was a error in Wikipedia (now corrected):
>
> in the definition of k-Wall-Sun-Sun prime p,
> V_p(k,-1) should be congruent to k (not 1 as it was stated earlier) modulo
> p^2.
>
> On Thu, Apr 21, 2016 at 12:44 PM, Richard J. Mathar <mathar at mpia-hd.mpg.de
> > wrote:
>
>> In response to
>> http://list.seqfan.eu/pipermail/seqfan/2016-April/016278.html :
>>
>> I don't understand the first terms in the Wikipedia article
>> https://en.wikipedia.org/wiki/Wall%E2%80%93Sun%E2%80%93Sun_prime .
>> The Lucas sequence of the second type V_n(2,-1) is A002203 at k=2.
>> V_2(2,-1)=6
>> V_3(2,-1)=14
>> ...
>> V_13(2,-1) = 94642
>>
>> Now 94642 mod (13^2) = 2, whereas according to the definition this needs
>> to
>> be 1 if 13 is supposed to be the smallest k-Wall-Sun-Sun prime for k=2
>> (?).
>> So according to the "alternative" definition 13 is *not* the smallest
>> 2-Wall-Sun-Sun prime.
>>
>> Also, the V_n(3,-1) sequence is A006497(n) and the term A006497(241) mod
>> 241^2
>> is 3, not 1.
>>
>> Richard
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>
```