[seqfan] Re: A006451 = n such that n*(n+1)/2+1 is square?

[Max Alekseyev]

On Sat, Oct 10, 2009 at 7:54 AM,  <franktaw at netscape.net> wrote:

> This suggests the following algorithm: factor 8k-1.  Discard any square
> factors (cf. A007913).  If any prime == 3 or 5 (mod 8) remains, there
> are no solutions.  (This is certain.)  If no such prime factor remains,
> there are solutions.  (This is conjecture).

Representation of primes by quadratic forms is well-studied subject.
Even is SeqFan we discussed it several times.
There cannot be any conjectures. ;)

Max