### Integer sequence review: A005114

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.

Following last week’s palaver, we’re going to do our best to be serious this time. Game faces on. David promises there will actually be some maths in this sequence.

#### A005114 Untouchable numbers: impossible values for sum of aliquot parts of $n$.

2, 5, 52, 88, 96, 120, 124, 146, 162, 188, 206, 210, 216, 238, 246, 248, 262, 268, 276, 288, 290, 292, 304, 306, 322, 324, 326, 336, 342, 372, 406, 408, 426, 430, 448, 472, 474, 498, 516, 518, 520, 530, 540, 552, 556, 562, 576, 584, 612, 624, 626, 628, 658, ...

### Integer sequence review: A051200

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’ll be rating sequences on four axes: NoveltyAestheticsExplicability and Completeness.

#### A051200 Except for initial term, primes of form “n 3’s followed by 1”.

3, 31, 331, 3331, 33331, 333331, 3333331, 33333331, 333333333333333331, 3333333333333333333333333333333333333331, 33333333333333333333333333333333333333333333333331, ...

### Integer sequence review: A010727

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’ll be rating sequences on four axes: Novelty, Aesthetics, Explicability and Completeness.

#### A010727 Constant sequence: the all 7’s sequence.

7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, ...

### Integer sequence review: A225143

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’ll be rating sequences on four axes: Novelty, Aesthetics, Explicability and Completeness.

#### A225143 Primes from merging of 10 successive digits in decimal expansion of $\zeta(2)$ or $\frac{\pi^2}{6}$.

9499012067, 4990120679, 3040043189, 1896233719, 2337190679, 9628724687, 2510068721, 8721400547, 9681155879, 5587948903, 7564558769, 9632356367, 3235636709, 3200805163, 4445184059, 3876314227, 2276587939, 1979084773, 9420451591, 9120818099, ...

### Art for a maths department

I don’t think the university maths department I work in has enough art in it. I have gazed covetously upon the walls of other departments I visit, covered with beautiful mathematically-inspired paintings and inspirational posters, serving as a backdrop to cabinets full of geometrical curiosities. I recently suggested to our Head of School that we could buy some art, and he said “That’s a good idea. Send me some suggestions.”

I was pretty delighted with that response, so I spent an enjoyable hour trawling the internet for art that would inspire and enrich our students and staff. We don’t really have anywhere obvious to put sculptures, so I wanted something you can hang on a wall. I had no idea how much money the Head of School was thinking of spending, so I assumed the worst and tried to stick to cheap posters and prints as a starting point. I wasn’t just looking for art – anything to decorate the walls, even if it ends up teaching the students something, is desirable.

My first port of call was my Arty Maths blog. I’ve been collecting nice bits of art that invoke or involve maths (and not art created purely to represent maths) for almost two years now. Unfortunately, it turns out I’ve almost exclusively been collecting sculptures and video works. That meant I had to do some googling!

Because I found some nice things, and in case anyone else is tasked with decorating a maths department and needs ideas, here’s what I found:

### Games to entertain a commutative mathematician.

I get the Tyne & Wear Metro in and out of work every day. When I don’t have a quality periodical to peruse, I like to play games on my phone. I’ve found a few really good games for my phone that also exercise my maths muscle recently, so I thought I’d write a post about them to share the fun, and prompt you to recommend even more.

Since I’ve got an Android phone, I’m no doubt missing some fantastic games on iOS, but lots of apps these days have versions for both big platforms. I’m also giving UK prices; prices in your country are likely the same numbers with different symbols in front.