Distribution of perfect powers: parabolic sections

[franktaw at netscape.net]

Not really a hand-wave; the argument can be made rigorous.

Franklin T. Adams-Watters

-----Original Message-----
From: Richard Guy <rkg at cpsc.ucalgary.ca>

Just a handwave --  As the perfect cubes and
higher powers are less dense than the squares,
there will be increasingly long such sequences.

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.
> ...
> 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"?

________________________________________________________________________
More new features than ever.  Check out the new AIM(R) Mail ! - 
http://webmail.aim.com