[seqfan] Re: FYI - conjecture: n=x^2+T_y+F_m

[Max Alekseyev]

On Tue, Dec 23, 2008 at 6:03 AM, Alexander Povolotsky
<apovolot at gmail.com> wrote:
>>These counterexamples belong to A115171.
>
> A115171 is seems tobe  restricted to positive only Fibonacci numbers
> while this particular conjecture (it appears to me) was allowing any
> (negative values included)  Fibonacci numbers.

No, the only difference from A115171 is allowance of zero Fiboncacci
number, meaning that (as I said above) all such counterexamples belong
to A115171.
In other words, they form a subsequence of A115171.

> That is why Giovanni Resta (if I understand his message correctly)
> only so far found just one counterexample against this particular
> conjecture.

The next counterexample 776218485 was recently mentioned in NMBRTHRY.

Max