Happy birthday to MC Hammer who, at age 52, is now mathematically untouchable.
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- 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.
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: Novelty, Aesthetics, Explicability 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, ...
OEIS contest for January AMS/MAA meeting
Top chap (and newest Aperiodipal?) Neil Sloane, founder of the Online Encyclopedia of Integer Sequences, wrote in to direct our attention towards a “best new integer sequence” contest being run on the sequence-fans mailing list.
Any sequence submitted between the middle of December and the middle of January is eligible. The winners (of which there will be at least three) will each receive a signed copy of the original 1973 Handbook of Integer Sequences, as well as the highly coveted “nice” keyword on their encyclopedia entries.
OEIS Foundation Appeal
If you’ve worked with or used any sequences of integers lately (and let’s face it, you have) you might have looked them up in the OEIS. I’ve used it twice today, and it’s still before 9.30am. As you may have gathered from our extensive banging on about it, we’re huge fans of the Online Encyclopedia of Integer Sequences.
If you have visited their site recently, you might have noticed an extra paragraph of red text near the top – yes, they’re doing a Wikipedia, and asking for their users (which is realistically everyone) to donate so they can keep going. It’s a hugely worthy cause, and here at the Aperiodical, we think it’s worth supporting. The OEIS is owned and maintained by The OEIS Foundation Inc., a nonprofit company.
Head over to the OEIS for lists of integers with various properties, and to find out more.
Integer sequence review: A006720
A006720
Somos-4 sequence: $a(0)=a(1)=a(2)=a(3)=1$; for $n \geq 4$, $a(n)=(a(n-1)a(n-3)+a(n-2)^2)/a(n-4)$.1, 1, 1, 1, 2, 3, 7, 23, 59, 314, 1529, 8209, 83313, 620297, 7869898, 126742987, 1687054711, 47301104551, 1123424582771, 32606721084786, 1662315215971057, 61958046554226593, 4257998884448335457, 334806306946199122193, ...
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:
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 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!