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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.

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.

DC: About cake?

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

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, ...

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 Ultimate Showdown

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.

[youtube url=http://www.youtube.com/watch?v=VDD6FDhKCYA]

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!

Links

Integest Sequence 2013 Public Vote

Numberphile

Dr Tony Padilla

Ipso Post Facto Navigato

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.

sunstroke

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

oeis review melee

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!