[seqfan] Re: A039669 and new related numbers

[Tomasz Ordowski]

Robert, thanks to you, we have the brilliantly simple
proof that there are no more such numbers from PS.

Now that this is proven - as I wrote - I can forget about OEIS,
because the data section {5, 8, 13, 20} is too weak, and...
the sequence would be of little interest, oh well.

However, my first numbers seem worthy
of a new sequence on the OEIS. Yes?
I hear no objection!

Best,

Tom Ordo

śr., 21 lut 2024 o 16:02 <israel at math.ubc.ca> napisał(a):

> There are no more of these.  If k - 2^2 = a^2 and k - 2^4 = b^2,
> then a^2 - b^2 = 12, and the only nonnegative integer solution of that is
> a = 4, b = 2 corresponding to k = 16.
>
> Cheers,
> Robert
>
> On Feb 21 2024, Tomasz Ordowski wrote:
>
>
> >PS. Similarly. Interesting, but with a poor data section, namely:
> >Numbers k such that all positive values of k - 2^(2^n) are square,
> >with natural n > 0. Data: {5, 8, 13, 20}. Please "more", if any...
> >Note that 2^(2^n) for n > 0 is the square (2^(2^(n-1))^2.
> >If there are no more terms, what do we do with it?
> >Prove it and forget about the OEIS. Yes?
> >
> >--
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> >
> >
>
>
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