## The On-Line Encyclopedia of Integer Sequences 63

Neil Sloane writes,

*"Run across a number sequence you want to identify? For instance, what comes next after 1, 2, 4, 9, 20, 48, 115, 286, 719, ...? The On-Line Encyclopedia of Integer Sequences is a database with over 50,000 such sequences. Serves as a "fingerprint file," so you can see if your problem has been studied before. Widely used by researchers in number theory, combinatorics, computer science, physics, chemistry, etc., as well as people trying to solve puzzles. "*That's nuts. Mind you it would in no way have assisted me in getting a decent grade in calculus, but still, it's fun.
## Didn't have 1,6,28,496,8128,... (Score:1)

Back in high school (mid 80s) we had very informal my-dick-is-bigger-than-yours type contests to see who could pointlessly waste the

mostamount of CPU time on the timeshared PDP-11 within a marking period. Every marking period, the system administrator would print out a list of the active accounts on the system, which showed total amount of time logged in, total amount of CPU time used, etc. If your account had the most CPU time, it was a (dubious) distinction. It meant you were working hard, I guess.So having compute-bound programs running all the time generating sequences like this one was a briefly popular craze.

Anyway, 1,6,28,496,8128 is as far as this sequence goes in 16-bit integers. But some of you out there might actually have 32-bit or 64-bit computers by now, so maybe this can be extended, if you know what the sequence is. Hint: it has to do with factors.

## Classify this! (Score:1)

(Actually that's a link to a pretty cool random number server. They also have links to some others based on radioactive decay, etc.)

## an answer (Score:1)

which also happens to be the german word for duck, believe it or not...

## Re:What comes next? (Score:1)

Either that, or I've totally scrambled my cache...

## This is old news... (Score:1)

-- Abigail

## Re:Interesting, but.... (Score:1)

anyanswers (I asked it for the top 30). So either their server is very incomplete, it's been slashdotted, or it was trying to calculate all possible answers before giving me back the top 30.## Re:Great for experimental music!!! (Score:1)

## Re:Great for experimental music!!! (Score:1)

Weak Monty Python reference...## Re:Thanks, Rob! (Score:1)

a cute little algorythm for extracting the

square root of a number.

## 6, 28, 496, 8128 : perfect numbers (Score:1)

## Re:Intelligence tests (Score:1)

## Re:Intelligence tests (Score:1)

## What comes next? (Score:1)

## Re:As long as we're talking about numbers... (Score:1)

> http://www.cecm.sfu.ca/projects/ISC/

Argh. NOW I found out about a home site, after I graduate. *sigh*

Another great site is Eric's Treasure Trove of Science

http://www.treasure-troves.com/ [treasure-troves.com]

Cheers

## Re:This will be so handy (Score:1)

--

## Re:Great for experimental music!!! (Score:1)

Number four. Number four. Number four. Number four. Number four. Number four.## Re:Another easy one to try.... (Score:1)

## A great general math site... (Score:1)

## Re:Try this one. (Score:1)

oops

## Re:Amazing! (Score:1)

POSTED: 11:52pm (TZ?)

FIRST POST: 10:38am EST

./ server responded to ping requests okay but I've been getting request time outs all day

Can anyone say DDoS?

## Quantum Physics and Relativity (Score:1)

Actually most branches of mathematics no matter how abstract have eventually found their way into physics or some other related scientific field. Does this not strike you as somewhat strange? I mean we devise up these crazy number theories and ideas and then they almost magically appear in nature to fit our mathmatical model.

Just some food for thought...

Nathaniel P. Wilkerson

NPS Internet Solutions, LLC

www.npsis.com [npsis.com]

## Re:Great for experimental music!!! (Score:1)

## Great! (Score:1)

## Potentially Better? (Score:1)

## Re:Amazing! (Score:1)

## Re:Amazing! (Score:1)

## Re:Interesting, but.... (Score:1)

## Re:Try this one. (Score:1)

## 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1... (Score:2)

## Re:What comes next? (Score:2)

Zilog had the Z8, Z80, Z800, Z8000 and Z80000. Then the company suffered a fatal arithmetic overflow trap.

## very useful (Score:2)

In a similar vein, and very interesting for coding theorists, is this page [win.tue.nl]. Set up by kernel and nethack hacker Andries Brouwer.

## Intelligence tests (Score:2)

Of course, as another poster stated, any given finite sequence has an infinite number of polynomials that can generate it and any other term you choose, which is why those types of questions tend to irritate me. The question should be qualified, as in, 'What is the next number in this sequence, assuming a simple generator for the sequence?' (Leaving room to quibble over the meaning of the word 'simple', naturally)

Definitely a very cool site, and I am glad to see this type of stuff here.

Since we are on the topic of sequences, and there was another article about puzzles, here's an old chestnut:

What is the next letter in the following sequence?

O T T F F S S

## This will be so handy (Score:2)

## 196884 and the Moonshine Conjecture (Score:2)

However, if you find a formula that "seems right", it may make it easier to prove that it *is* right, because now you're barking up the right tree.

An example of this happening in real life is the number 196884. It turned up in two seemingly unrelated places, in the character table of the Monster Group and in the expansion of the j function. This lead mathematicians to search for - and find - the connection between the two.

See Scientific American [sciam.com] for a good article about this "Moonshine Conjecture".

## Re:Great for experimental music!!! (Score:2)

## Very useful for prior papers and references (Score:2)

## Try this one. (Score:2)

## Great for experimental music!!! (Score:2)

## Interesting, but.... (Score:2)

## Musical theme dictionary (Score:3)

The paper they wrote is Smith, Lloyd A., Rodger J. McNab and Ian H. Witten. Sequence-based melodic comparison: a dynamic-programming approach. In Hewlett, Walter B. and Eleanor Selfridge-Field (eds.) Melodic Similarity: Concepts, Procedures, and Applications, Computing in Musicology 11, Chapter 4, 1998, p 101--117.

Check out http://www.nzdl.org/cgi-bin/gwmm?c=meldex&a=page&

## Re:Thanks, Rob! (Score:3)

I know of two "generators" for triplets, but I don't think it is helpful for the x^2, (x+1)^2 series (except in the very basic case of 3-4-5).

Anyway, for all natural numbers n:

If n is odd, then n, floor(n^2/2), ceil(n^2/2) is a triplet.

If n is even, then n, (n/2)^2-1, (n/2)^2+1 is a triplet.

A little algebra will show why these are true, but it is interesting how it starts by catching some of the better known triplets.

(3-4-5, 5-12-13, 7-24-25, 8-15-17, etc.)

Now if only the site becomes un/.ed, I might not get any work done today.

----

## But it's badly broken! (Score:4)

99 bottles of beer on the wall..., but it failed to even parse the request. So I simplified it to the integer values in the first six-pack:99, 98, 97, 96, 95, 94. This time it parsed the request, but said the sequence wasn't in its database! What good is this site if it doesn't event recognize the beer sequence?--Jim

## I've used this... (Score:4)

Another interesting idea that I've seen printed is a musical theme dictionary, if you can plunk out the first few notes by ear then you can look up the sequence. Has anyone done this online? Would someone sue you for it, since printed and/or recorded music is a pretty touchy subject on the Internet.

My favourite sequence, not listed, is:

s(n)

n=1,2,3,4,... is the number of people in an elevator and, if one of them farts, s(n) is the number of people who are

surewho did it.Alan.

## Thanks, Rob! (Score:4)

I just wanted to say thanks to Rob for running this one though - I found the significance of a very interesting series which is related to the solution to:

x^2 + (x+1)^2 = z^2 (x,z in natural numbers)

That series is: 1,3,7,17,41,99,239,577,1393,3363,...

Each subsequent number in the series converges on a multiple of the previous one, but according to the site the series is also the numerators in the continued fraction expansion of the square root of two.

(Score -1: Boring)

## If you were wondering... (Score:4)

Sequence: 0,1,1,2,4,9,20,48,115,286,719,1841,4755,12410,325

Name: n-node rooted trees of height at most 9.

Links: Index entries for sequences related to rooted trees Transforms

Formula: Take Euler transform of A034825 and shift right. (Christian G. Bower (bowerc@usa.net)).

See also: See A001383 for details.

Keywords: nonn

Offset: 0

Author(s): njas

## As long as we're talking about numbers... (Score:5)

Another great resource is the Inverse Symbolic Calculator [cecm.sfu.ca]. Take that real number you've been trying to identify, and see what formula or combination of known constants might have generated it.

The integer sequence database has proven quite handy to me on several occasions. Kudos to N. J. A. Sloane for creating and maintaining it, and to the people who keep contributing more good sequences!

-jason

"If you're not part of the solution, you're part of the precipitate."

## Get the book! (Score:5)