# [seqfan] Aaron David Fairbanks : Pappus Chain Sequence (by way of moderator)

Olivier Gerard olivier.gerard at gmail.com
Tue May 13 15:21:57 CEST 2014

```From: Aaron David Fairbanks <unknownthingamabob at gmail.com>
To: Seqfan <seqfan at list.seqfan.eu>
Date: Sat, 10 May 2014 18:54:19 -0400
Subject: Pappus Chain Sequence

Hi Seqfans,

I couldn't help but notice that the sequence exhibited by this Numberphile
video (http://www.youtube.com/watch?v=sG_6nlMZ8f4) has not been submitted
to the OEIS:

15, 23, 39, 63, 95...

It is defined as the denominators of the sequence of ratios between blue
circles' radii and the outer circle's radius in the following diagram (a
Pappus chain where the radius of the inner circle is 1/2 the radius of the
outer circle):

i.e. the largest blue circle has 1/15 the radius of the enclosing circle,
the 2nd largest has 1/23, and so on. If you can't view this image, the
Numberphile video does a good job explaining it.
​

I am a completely amateur math enthusiast, and I'm not at all familiar with
this field of math, but I was interested by this video. Is the sequence
worth noting? OEIS tells me it "appears to be + 4x^2 - 4x + 15," but I
don't know if this is true, or how I would go about proving it. Should I
work on submitting it anyway? If so, how would I give a more technical
definition of these "blue circles"?

I'm sure there are many other related sequences in the same vein as this
one, that might be interesting to explore. I haven't looked into any of
them on my own yet, but feel free to give it a go if you see some potential.

This is my first exchange with the Seqfan mailing list, so let me know if
I'm doing anything completely wrong.

Thanks everyone,
Aaron Fairbanks
```