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

[Max Alekseyev]

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
>
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