[seqfan] Re: What is in a name? A161621

Charles Greathouse charles.greathouse at case.edu
Fri Dec 13 15:43:09 CET 2013

```"Numerator of (pi((n+1)^2) - pi(n^2)) / (pi((n+2)^2) - pi(n^2))."

"Numerator of (x-y)/(z-y), where x = pi((n+1)^2), y = pi(n^2), and z =
pi((n+2)^2)."

"Numerator of (b(n+1) - b(n))/(b(n+2) - b(n)), where b(n) = A038107(n) is
the number of primes up to n^2."

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Dec 13, 2013 at 9:27 AM, John W. Nicholson
<reddwarf2956 at yahoo.com>wrote:

> I don't know where to start. Can someone simply this title?
>
> (blue bar)
> A161621     Numerators of the ratios (in lowest terms) of numbers of
> primes in one square interval to that of the interval and its successor.
> The numerators are derived from sequence A014085. The expression is:
> R(n)=(PrimePi[(n+1)^2] - PrimePi[n^2])/(PrimePi[(n+2)^2] - PrimePi[n^2]);
> The first few ratios are: 1/2, 2/5, 3/5, 1/3, 4/7,...
> (blue bar ends)
>
>
> John W. Nicholson
>
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>
```