Distribution of perfect powers: parabolic sections

zak seidov zakseidov at yahoo.com
Thu Feb 21 17:57:22 CET 2008

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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