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## The Connoisseur of Number Sequences63

An anonymous reader writes: 75-year-old Neil Sloane is considered by many to be one of the most influential mathematicians of our time, not because of the theorems he's proved, but because of his creation: The Online Encyclopedia of Integer Sequences (OEIS). Quanta Magazine reports: "This giant repository, which celebrated its 50th anniversary last year, contains more than a quarter of a million different sequences of numbers that arise in different mathematical contexts, such as the prime numbers (2, 3, 5, 7, 11 ) or the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13 ). What's the greatest number of cake slices that can be made with n cuts? Look up sequence A000125 in the OEIS. How many chess positions can be created in n moves? That's sequence A048987. The number of ways to arrange n circles in a plane, with only two crossing at any given point, is A250001. That sequence just joined the collection a few months ago. So far, only its first four terms are known; if you can figure out the fifth, Sloane will want to hear from you."
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## The Connoisseur of Number Sequences

• #### A250001 (Score:2, Funny)

by Anonymous Coward

COMMENTS a(5) reduced by 1 because of a takedown order by the IOC for their trademarked 5-ring configuration.

• #### 50th anniversary "on-line"? (Score:5, Informative)

on Friday August 07, 2015 @08:39AM (#50268351) Homepage

If you're wondering how an "on-line" collection celebrated its 50th anniversary recently: the collection was begun in 1964; it was made available via the Internet starting in 1996.

• #### Re: (Score:1)

He started collecting them in 1965, " This giant repository, which celebrated its 50th anniversary "

• #### 75-year-old Neil Sloane is considered by many (Score:2, Insightful)

by Anonymous Coward

Who are these "many"? Horrible journalism.

• #### Re: (Score:3)

Who are these "many"? Horrible journalism.

Probably talking about people like me, who have saved many hours of effort multiple times per year since discovering it over a decade ago.

• #### Re: (Score:2)

And me: I first found it as a hardcover book "a handbook of integer sequences" about 25 years ago.

• #### Re: (Score:2)

Probably talking about people like me, who have saved many hours of effort multiple times per year since discovering it over a decade ago.

Or people like me that often browse through the OEIS for fun, and learn lots of cool stuff from the extensive references.

• #### Re:75-year-old Neil Sloane is considered by many (Score:5, Informative)

on Friday August 07, 2015 @12:25PM (#50269877) Homepage
Mathematicians. I don't how many times I've seen a sequence of integers and then gone to Sloane's encyclopedia to see if the sequence is known. This is helpful in both not duplicating others work (e.g. finding out that something one has found is already known) or b) identifying that a given sequence is a known sequence and then using that as a guideline on what to prove. That last bit happens surprisingly often when one has combinatorial structure to something: pop the sequence of numbers you've got into his database and it will tell you something like the first 6 terms matching some nice combinatorial thing and then you can with that guidance go and prove that in general that's what the sequence really is.
• #### Re:75-year-old Neil Sloane is considered by many (Score:4, Informative)

on Friday August 07, 2015 @01:46PM (#50270453) Homepage

Who are these "many"? Horrible journalism.

Unsurprisingly, mathematicians. Many mathematicians use the OEIS frequently, heck experts and professionals from other disciplines like Computer Science, Economics, or Physics routinely use OEIS to identify numeric sequences or patterns.

I'd hazard to say anyone who calls themselves a mathematician has used OEIS (or the book version) at least once. In fact I'd be surprised if you could find anyone with a graduate degree in mathematics who doesn't know who Neil Sloane or OEIS are.

Yes, it is that important.

• #### pseudo-base-prime (Score:2)

OEIS is great. I started working on a project and was able to find some other work done on the same sequence(s)... ,3,5,9,7,15,11,27,... [oeis.org] -- my project [livejournal.com] concerns representing the positive integers in terms of their prime factorization and then examining the properties of various operations on this representation. =)
• #### Re: (Score:2)

Any of you old timers remember the Chemical Rubber Handbook? It's a site now also:
http://www.hbcpnetbase.com/ [hbcpnetbase.com]

• #### Re: Handbooks (Score:3)

Any of you old timers remember the Chemical Rubber Handbook? It's a site now also:
http://www.hbcpnetbase.com/ [hbcpnetbase.com]

I admit I've always heard it called the CRC Handbook(s). The "original" being their Chemistry and Physics one (the one at the link), though CRC Press does tons of technical, scientific printing in the US, they also have handbooks on topics in computer science [crcpress.com], computer security and many others.

And my copy is I think 80-something-th edition.

• #### Re: (Score:2)

I still refer regularly to my CRC Standard Math Tables—two different editions, both sadly decades out of date.

I was tickled years ago to discover the OEIS; some other math website referred to it, and I was lost for hours. TV Tropes for math nerds.

• #### One of the worst words in the english language (Score:1)

Maybe it's because i also speak french (but neither english nor french are my native language), but connoisseur.... wtf. When i first heard it used in Futurama, i actually thought it was a small joke of an english speaker completely mispronouncing a french (connaisseur) word, trying to sound smarter than he was, but it's an actual english word 0_0. I cringe every time i hear or read it.

• #### Re: (Score:1)

by Anonymous Coward

That was actually the correct French spelling at the time when it was borrowed into the English language.

• #### Re: (Score:3)

You do realize that the French language has changed the spelling of many of its words over the centuries? Glancing through the online dictionaries, it appears the word "connoisseur" entered the English language around the beginning of the 18th century, 300 years ago. And there's some French words that came over with William the Conqueror almost a millennium ago.

• #### I thought this was America (Score:2)

If Neil Sloane is so smart, why ain't he rich?

Let me know when his list includes the number sequence for tomorrow's Lotto.

• #### Re: (Score:2)

I'm sure it's in there somewhere. You just have to know where to look.
• #### Re: (Score:2)

If Neil Sloane is so smart, why ain't he rich?

Let's see, they say that "Knowledge is Power", so knowledge = power, and we know from physics that power = work / time. And finally, they say that "Time is money", so time = money.

So, making the substitutions: knowledge = work / money, and solving for money, money = work / knowledge.

So, now we can see that the dumber you are, the more money you can make!

• #### Re: (Score:2)

"So, now we can see that the dumber you are, the more money you can make!"

i.e; the mafia, Dubya, Brittany Spears, etc.

An explanation. [feelingsuccess.com]
• #### Re: (Score:2)

"So, now we can see that the dumber you are, the more money you can make!"

i.e; the mafia, Dubya, Brittany Spears, etc.

So says someone who uses "i.e." when the proper term in this case is "e.g."

• #### Re: (Score:2)

Don't come down on him; he obviously is angling for a raise.

• #### Before there was the interwebs (Score:1)

There was the HandBOOK of Integer Sequences.
Some of my math professors are probably still wondering how I solved those extra credit problems :)
It was good for party tricks are well, at the right sort of party obviously.

• #### Elevator sequence (Score:5, Funny)

on Friday August 07, 2015 @11:42AM (#50269521)

I like the sequence: 1,2,1,1,1,1 ...

The X axis is the number of people in an elevator.
The Y axis is how many people know which one farted.

• #### Do they have... (Score:2)

1 - 2 - 3 - 4 - 5, which is commonly used for luggage combinations and planetary shields?

• #### Re: (Score:2)

Yes, that's A000027 [oeis.org].

• #### Re: (Score:2)

000027? That's the combination to my luggage!
• #### Re: (Score:2)

I spent weeks writing a program to expand that list to 1000 items and oeis.org wouldn't accept it.

Snobs.

• #### More practical application ... (Score:2)

... as a practice exercise for optimization.

Mike Acton gave an excellent talk Code Clinic 2015: How to Write Code the Compiler Can Actually Optimize where he picked an integer sequence to optimize the run-time to calculate the sequence. Techniques include: memoization, and common sub-term recognition. For 20 values pre-optimization time was: 31 seconds, post-optimization time was: 0.01 seconds.

* https://youtu.be/GPpD4BBtA1Y?t... [youtu.be]

Original GDC Talk

* http://gdcvault.com/play/10218... [gdcvault.com]

• #### Number of arrangements of n circles... (Score:2)

Number of arrangements of n circles in the affine plane:

1, 1, 3, 14, 168, ...

If anyone cares, the next number in this sequence is 3172. And no, I did not brute force it, I examined the problem symmetry.

• #### Re: (Score:2)

You mean like that the next value after that is 91958?

And the one after that 3402408?

}B^)

• #### Re: (Score:1)

Like your high school math teacher would, I give you a grade of zero for those answers.
• #### Re: (Score:2)

Yes, I understood that you were implying that you wanted:

(1) A description of the realization
(2) The process by which I arrived at the realization ("show your work")
(3) A description of the algorithm, process, or formula used to obtain the next number in the sequence given the previous numbers as a clue

Why don't we wait for brute force verification as to whether or not I'm correct, shall we? If that verification happens, I will happily describe those three points, and ruin a perfectly good (so far) crypto

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