My son was born last September. While he doesn’t hate sleep as much as his sister did, he still needs a bit of help to drop off.
I’m not at all musically inclined, and I seem unable to remember more than a couple of lines from wordy songs (my version of “Papa’s gonna buy you a mockingbird” rapidly veers into nonsense as I try to think of a rhyme for the next line), so when the girl was little I hit upon the strategy of singing counting songs to lull her off to sleep.
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
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, ...
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, ...
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
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!
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!