[seqfan] Re: A018805 optimizations

[Neil Sloane]

This is classical number theory - see Hardy and Wright, Theorem 332.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Jan 20, 2017 at 8:06 AM, M. F. Hasler <seqfan at hasler.fr> wrote:

> On Thu, Jan 19, 2017 at 9:36 AM, David Wilson <davidwwilson at comcast.net>
> wrote:
>
> > For a while I've had an idea for optimizations for A018805(n) = { 1 <= x
> <=
> > n, 1 <= y <= n, gcd(x, y) = 1 }.
> > I was able to compute a(n) for powers of 10 up to 10^12 in a few minutes.
> > I
> > got
> > ...
>
> 1e12 607927101854119608051819
> >
>
> The sequence c(n)/100^n =
> (1, .63,
> .6087, .608383, .60794971, .6079301507, .607927104783, .60792712854483,
> .6079271032731815, .607927102346016827, .60792710185772432731,
> .6079271018566772422279, .607927101854119608051819,
> ...)
> seems to converge to
> A059956 <https://oeis.org/A059956> Decimal expansion of 6/Pi^2.
>
> Of course, this is maybe just a coincidence (to 11+ digits....?)
>
> Maximilian
>
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