[seqfan] Re: Arithmetic progressions of squares

Moshe Levin moshe.levin at mail.ru
Mon Oct 24 16:12:35 CEST 2011

```One infinite set of triples is {1,x^2,2x^2-1} with x(1)=5,x(2)=5,x(n)=6x(n-1)-x(n-2)....
and I'd guess beforehand it's known:

A001653   Numbers n such that 2*n^2 - 1 is a square.

Regards, ML

24 октября 2011, 15:44 от Reinhard Zumkeller <reinhard.zumkeller at gmail.com>:
> ... please have a look at https://oeis.org/draft/A198384 .. A198390 (still
> in limbo). Later I will also try the second part (restricted triples).
>
> Best
> Reinhard
>
> 2011/10/24 Benoît Jubin <benoit.jubin at gmail.com>
>
> > Dear Seqfans,
> >
> > There does not seem to be OEIS sequences listing arithmetic
> > progressions of squares. The triples are characterized in
> > and it is shown that there is no arithmetic progression of four squares in
> > (I saw these papers while reading this question:
> > http://mathoverflow.net/questions/78949/arithmetic-progressions-of-squares
> > )
> >
> > It would be nice if someone could list these triples (ideally(?):
> > smallest, middle, largest elements, common differences, corresponding
> > smallest, middle, largest arguments; and the same restricting to
> > triples which are not multiples of smaller ones).
> >
> > Benoit
> > PS: I'm sorry this email sounds a bit like "please do that for me",
> > but (1) I really don't have time right now (2) it would take me much
> > more time to write a program to list and order them than most people
> > here (3) at least now the request is written somewhere, and if no one
> > finds time for it, I might do it next semester when I have more time.
> > So I thought it was still better to write this email than do nothing.
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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```