[seqfan] Re: A039669 and new related numbers

[israel at math.ubc.ca]

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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