### Integer Sequence Review – Sloane’s birthday edition!

The Online Encyclopedia of Integer Sequences contains over 200,000 sequences. It contains classics, curios, thousands of derivatives entered purely for completeness’s sake, short sequences whose completion would be a huge mathematical achievement, and some entries which are just downright silly.

For a lark, David and I have decided to review some of the Encyclopedia’s sequences. We’re rating sequences on four axes: Novelty, Aesthetics, Explicability and Completeness.

CP: It’s Neil Sloane’s 75th birthday today! As a special birthday gift to him, we’re going to review some integer sequences.

DC: His birthday is 10/10, that’s pretty cool.

CP: <some quick oeis> there’s a sequence with his birthdate in it! A214742 contains 10,10,39.

DC: We can’t review that. It’s terrible.

CP: I put it to you that you have just reviewed it.

DC: Shut up.

CP: Anyway, I’ve got some birthday sequences to look at.

CP: No.

#### A050255 Diaconis-Mosteller approximation to the Birthday problem function.

1, 23, 88, 187, 313, 459, 622, 797, 983, 1179, 1382, 1592, 1809, 2031, 2257, 2489, 2724, 2963, 3205, 3450, 3698, 3949, 4203, 4459, 4717, 4977, 5239, 5503, 5768, 6036, 6305, 6575, 6847, 7121, 7395, 7671, 7948, 8227, 8506, 8787, 9068, 9351

### Some more games to entertain a commutative mathematician

A while ago I collected a few of the mathsy games I play on my phone to while away my commute. I’ve found a few new ones since then, so I thought I’d do a new post to tell you about them.

Here’s a fun thing I found: the Journal of Number Theory has a YouTube channel on which it publishes video abstracts of its papers. To my surprise, they’ve been doing it since 2008!

### James Grime’s house-building problem

Aperiodipal James Grime has put a new video on his YouTube channel. He’s got a problem to do with building houses:

I was involved, that’s what! The puzzle can be done on pen and paper but it involves a lot of drawing and calculating, so James asked if anyone could make a computery version. I spent my day off work last week making just such a thing: the computerised Building Houses Problem.

### Everyone’s a mathematician

This morning Katie and I had a little discussion about house style on The Aperiodical. Mathematican Paul Taylor was listed as “Mathematician Paul Taylor” in the blurb for his featured post. I posited that everyone published here is a mathematician, so the “Mathematician” title is redundant.

This of course resulted in me writing a userscript which automatically prepends every name on the page with the honorific “Mathematician”.

### Integer sequence review: A193430

The Online Encyclopedia of Integer Sequences contains over 200,000 sequences. It contains classics, curios, thousands of derivatives entered purely for completeness’s sake, short sequences whose completion would be a huge mathematical achievement, and some entries which are just downright silly.

For a lark, David and I have decided to review some of the Encyclopedia’s sequences. We’re rating sequences on four axes: NoveltyAestheticsExplicability and Completeness.

This is the triumphant return of the integer sequence reviews!

#### A193430 Primes p such that p+1 is in A055462.

23, 6911, 5944066965503999, ...

### Babbage’s difference engine is really, really pretty

Hands up if you knew there was a working replica of Babbage’s difference engine in California.

(My hand is not up.)

This glorious machine lives in the Computer History Museum in Mountain View, California. A company called xRez Studio, which specialises in taking extremely high resolution gigapixel photos of things, has taken some extremely high resolution gigapixel photos of the difference engine. They’re so lovely that it feels wrong to be looking at them at work.