Distribution of perfect powers: parabolic sections

[Richard Guy]

Just a handwave --  As the perfect cubes and
higher powers are less dense than the squares,
there will be increasingly long such sequences.
[there are shades of the now-settled Catalan
conjecture and the abc-conjecture]    R.

On Thu, 21 Feb 2008, zak seidov wrote:

> Distribution of perfect powers A001597 has an
> interesting pattern:
> there are many (rather long) runs with
> the constant second difference equal to 2.
>
> The longest such run (among first 10000 terms) is
> A001597(9697..9759) with 63 terms.
>
> These terms are (naturally)
> the squares of subsequent integers (9230..9292),
> of which one itself is perfect power, 9261=21^3.
>
> Are there longer runs of perfect squares,
> "not allowing other perfect powers between them"?
>
> thanks, zak
>
>
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