### Integer Sequence Review Mêlée Hyper-Battle DX 2000, THE GRAND FINALE

Welcome to the Field of Dreams. Talking of which: why can’t you grow wheat in $\mathbb{Z}/6\mathbb{Z}$?

Anyway, we’re finally here: the Grand Finale of our tournament to find the Integest Sequence 2013. Here’s a reminder of the sequences vying for the title:

• From Bracket 1: A002210, the decimal expansion of Khintchine’s constant.
• From Bracket 2: A001220, the Wieferich primes.
• From Bracket 3: A001462, Golomb’s sequence.
• From Bracket 4: A023811, the largest metadromes in base $n$.
• From the first round of reviews, we picked the one whose score we fiddled the least: A010727, all the 7s.
• And the wildcard is A058883, the wild numbers.

It’s a been a long, hard battle. We’ve seen some good sequences, some bad sequences, and an awful lot of plagiarised GIFs. So, without further ado, it’s time to start the

### Integer sequence reviews on Numberphile (or vice versa)

There’s no new integer sequence review this week, because David and I are taking a break before the Grand Finale Ultimate Showdown of Dreams next week. To tide you over, top chap Brady Haran has recorded a Numberphile video with Tony Padilla explaining each of the six sequences in the final in his Enthusiastic Maths Outreach™ voice.

If you haven’t made your mind up yet, maybe the video will sway you. Or will it sow doubt into your previously made-up mind???!?!?!?!!?!?! Anyway, it’s a very good video.

The Integest Sequence 2013 will be announced next week in a glitzy celebrity gala event. There’s still time to vote for your favourite sequence, and there’s still time for us to decide how much attention we’ll pay to your vote. Everything’s still to play for!

Numberphile

### Integer Sequence Review Mêlée Hyper-Battle DX 2000 (Bracket 4)

Last week, A001462 – Golomb’s sequence – booked its place in the final. In retaliation for last week’s palaver, this week Christian has picked all the sequences. Unfortunately, the British Summer is happening today so we’re failing a bit, intellectually.

With that in mind, it’s time for round 4 of…

Here are the rules: we’re judging each sequence on four axes: Aesthetics, Completeness, Explicability, and Novelty. We’re reviewing six sequences each week for four weeks, picking a winner from each. Then, we’ll pick one sequence from the ones we reviewed individually before this thing started, plus a wildcard. Finally, a single sequence will be crowned the Integest Sequence 2013!

### Integer Sequence Review Mêlée Hyper-Battle DX 2000 (Bracket 3)

Last week, A001220 – the Wieferich primes – booked its place in the final. This week, David has picked six sequences all on his own to form Bracket 3 of…

Here are the rules: we’re judging each sequence on four axes: Aesthetics, Completeness, Explicability, and Novelty. We’re reviewing six sequences each week for four weeks, picking a winner from each. Then, we’ll pick one sequence from the ones we reviewed individually before this thing started, plus a wildcard. Finally, a single sequence will be crowned the Integest Sequence 2013!

### Integer Sequence Review Mêlée Hyper-Battle DX 2000 (Bracket 2)

Last week A002210, the decimal expansion of Khintchine’s constant, emerged victorious from Bracket 1. Now, get ready for round 2 of…

Here are the rules: we’re judging each sequence on four axes: Aesthetics, Completeness, Explicability, and Novelty. We’re reviewing six sequences each week for four weeks, picking a winner from each. Then, we’ll pick one sequence from the ones we reviewed individually before this thing started, plus a wildcard. Finally, a single sequence will be crowned the Integest Sequence 2013!

### Ghost Diagrams

Yet another fun toy for you. Give a computer a set of tiles defined by what their edges look like, can you fit them together? That problem is undecidable, since you can encode Turing machines as sets of tiles, but it turns out it’s fun to watch a computer try.

Ghost Diagrams asks you for a set of tiles (or it’ll make some up if you didn’t bring one) and shows you its attempts to make them fit together. It’s very pretty, and quite mesmerising. Sometimes it looks even better when you turn on the “knotwork” option.

Paul Harrison created Ghost Diagrams while writing his PhD thesis, Image Texture Tools: Texture Synthesis, Texture Transfer, and Plausible Restoration. He’s written a short blog post about the program.

Here are a few patterns I liked: 1, 2, 3, 4, 5.