You're reading: Posts Tagged: oeis

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

Discovering integer sequences by dealing cards

card dealing

Let’s play a game:

  1. Imagine you have some playing cards. Of course if you actually have some cards you don’t need to imagine!
  2. Pick your favourite natural number $n$ and put a deck of $n$ cards in front of you. Then repeat the next step until the deck is empty.
  3. Take $2$ cards from the top of the deck and throw them away, or just take $1$ card from the top and throw it away. The choice is yours.

If you pick a small $n$, such as $n=3$, it’s pretty easy to see how this game is going to play out. Choosing to throw away $2$ cards the first time means you’re then forced to throw away $1$ card the next time, but only throwing away $1$ card the first time leaves you with a choice of what to throw away the next time. So for $n=3$ there are exactly $3$ different ways to play the game: throw $2$ then $1$, throw $1$ then $2$, or throw $1$ then $1$ then $1$.

Now, here comes the big question. How does the number of different ways to play this game depend on the size of the starting deck? Or in other words, what integer sequence $a_0$, $a_1$, $a_2$, $a_3$, $a_4$, … do we get if $a_n$ represents the number of different ways to play the game with a deck of $n$ cards? (We already know that $a_3=3$.)

MC Hammer is mathematically untouchable

mchammermchammermchammermchammermchammer

Happy birthday to MC Hammer who, at age 52, is now mathematically untouchable.

1236681958_hammer-time

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, ...

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.

Google+