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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

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

Roger Apéry - 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.

Integer Sequence Reviews: A075771, A032799, A002717

It’s been almost two years since I last sat down with my friend David Cushing and did what God put us on this Earth to do: review integer sequences.

This week I lured David into my office with promises of tasty food and showed him some sequences I’d found. Thanks to (and also in spite of) my Windows 10 laptop, the whole thing was recorded for your enjoyment. Here it is:

I can only apologise for the terrible quality of the video – I was only planning on using it as a reminder when I did a write-up, but once we’d finished I decided to just upload it to YouTube and be done with it.

Are you sure 51 isn’t prime? – Analysing the results of the “Is this prime?” game

Two months ago, I bought and not only set up the internet’s fanciest primality-checking service, but also invented a rather addictive game.

It quite quickly went viral, or as relatively viral as a maths game can get, with people tweeting their high scores and posting the link to reddit and Hacker News. I realised fairly soon that I should put in some stats tracking, to see if there were any interesting patterns in the data (and also to inflate my ego as the “games played” counter went up). I missed the first big spike in traffic, but on the 9th of March I wrote a script which saved a record of each game to a database.

isthisprime game dates

The mad rush settled down quite quickly but there were still occasional spikes as different sites or people with lots of twitter followers found the game. Now, after two months, I’ve got data for just under 350,000 games. That’s a decent amount of information!