### Apéryodical: Roger Apéry’s Mathematical Story

This is a guest post by mathematician and maths communicator Ben Sparks.

## Roger Apéry: 14th November 1916 – 18th December 1994

100 years ago (on 14th November) was born a Frenchman called Roger Apéry. He died in 1994, is buried in Paris, and upon his tombstone is the cryptic inscription:

$1 + \frac{1}{8} + \frac{1}{27} +\frac{1}{64} + \cdots \neq \frac{p}{q}$

Apéry’s gravestone – Image from St. Andrews MacTutor Archive

Roger Apéry – Image from St. Andrews MacTutor Archive

The centenary of Roger Apéry’s birth is an appropriate time to unpack something of this mathematical story.

### Puzzlebomb – November 2016

Puzzlebomb is a monthly puzzle compendium. Issue 59 of Puzzlebomb, for November 2016, can be found here:

The solutions to Issue 59 will be posted at the same time as issue 60.

Previous issues of Puzzlebomb, and their solutions, can be found at Puzzlebomb.co.uk.

### The magic number 25641

Reader of the site Bhaskar Hari Phadke has written in to tell us this fun fact about the number $25641$. It’s easier to show than to describe, so here goes:

\begin{align}
25641 \times \color{blue}{1} \times 4 &= \color{blue}{1}02564 \\
25641 \times \color{blue}{2} \times 4 &= \color{blue}{2}05128 \\
25641 \times \color{blue}{3} \times 4 &= \color{blue}{3}07692 \\
25641 \times \color{blue}{4} \times 4 &= \color{blue}{4}10256 \\
25641 \times \color{blue}{5} \times 4 &= \color{blue}{5}12820 \\
25641 \times \color{blue}{6} \times 4 &= \color{blue}{6}15384 \\
25641 \times \color{blue}{7} \times 4 &= \color{blue}{7}17948 \\
25641 \times \color{blue}{8} \times 4 &= \color{blue}{8}20512 \\
25641 \times \color{blue}{9} \times 4 &= \color{blue}{9}23076
\end{align}

A good one to challenge a young person with.

I did a little bit of Sloanewhacking and found a couple of sequences containing $25641$ which almost, but don’t quite, describe this property. So, semi-spoiler warning: you might enjoy A256005 and A218857. I’d like to come up with the ‘magic number’ which looks the least like it’ll have this property – any ideas?

### Carnival of Mathematics 139

The next issue of the Carnival of Mathematics, rounding up blog posts from the month of September, and compiled by Manjil, is now online at Gonit Sora.

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

### “π – It’s Complicated” – a talk I gave on Pi Day 2016 at Ustinov College Café Scientifique

I was invited to give a talk for Ustinov College’s Café Scientifique on π Day this year. The turnout wasn’t great and I put quite a bit of effort into the slides, so I wanted to put it online. I’ve finally got hold of the recording, so here it is. Unfortunately they didn’t set the camera’s exposure properly, making the screen illegible, so you’ll probably want to follow along with the slides in another window.

I tried to come up with a way of writing today’s date as a multiple of π Day, but couldn’t make it work. However, I did realise that Halloween (31/10) is the best approximation to π between now and the next π day (I think). Sπooky!

### Maths at the Manchester Science Festival 2016

Here’s our annual round-up of what’s happening in sums/thinking at this year’s Manchester Science Festival. If you’re local, or will be in the area around 20th-30th October, here’s our picks of the finest number-based shows, talks and events.

### Puzzlebomb – October 2016

Puzzlebomb is a monthly puzzle compendium. Issue 58 of Puzzlebomb, for October 2016, can be found here:

The solutions to Issue 58 can be found here:

Previous issues of Puzzlebomb, and their solutions, can be found at Puzzlebomb.co.uk.