Sequences based on algorithms

[Max Alekseyev]

On Nov 15, 2007 11:16 AM, Max Alekseyev <maxale at gmail.com> wrote:
> On Nov 14, 2007 11:14 PM, Jonathan Post <jvospost3 at gmail.com> wrote:

> > %I A000001
> > %S A000001 6, 35, 143, 391, 899, 1739, 3233, 5293, 8051, 11413, 17653,
> > 24883, 33389, 43931, 56977, 72731, 92881, 118829, 145699, 176039
> > %N A000001 Smallest prime between n^2 and (n+1)^2 times largest prime
> > between n^2 and (n+1)^2.
> > %C A000001 First 5 values are a subset of A132435.
>
> This is always the case.
> Let p and q be the smallest and largest primes in the interval [n^2,(n+1)^2].
> Then
>
> n^2 < p < q < (n+1)^2

I forgot to mention that in the case p=q the statement is trivial.
So in my proof I assume p < q.

Max