[seqfan] Re: Question from Harvey Dale about A233552

M. F. Hasler seqfan at hasler.fr
Tue May 28 00:41:55 CEST 2019

```I added Robert's proof that sequence A233552 is wrong (not only probably),
after correcting 373 to 361 (this confused me for a moment, also w.r.t. his
next message...)
and changed the status from "uned,obsc" to "dead".
The fact that all odd squares not multiple of 3 are solutions but only very
few of these are listed,
suggests that the author may have considered excluding these.
I think it would be nice to have both correct versions, with and without
odd squares.
- Maximilian

On Sun, May 26, 2019 at 7:47 PM <israel at math.ubc.ca> wrote:

> Note that if n=m^2 is a square, n*4^k-1 = (m*2^k-1)*(m*2^k+1), so (if
> m*2^k-1 > 3) (n*4^k-1)/3 must be composite. Thus 25, 49, 121, 169, 289,
> 373, 529, 625, 751, 841, 961 should certainly be in the sequence.
>
> Cheers,
> Robert
>

> On May 26 2019, Neil Sloane wrote:
>
> >Harvey just asked me the following question.  Can anyone help
> >
> >I may be missing something, but there seem to be many terms missing from
> >the above sequence. My calculations show that, up to 1000, each of 25, 49,
> >121, 169, 289, 361, 373, 499, 529, 613, 625, 751, 841, 919, and 961
> >satisfies the definition, but only 361 and 919 appear in the data.

```