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The On-Line Encyclopedia of Integer Sequences

Posted by CmdrTaco on from the that's-six-times-10-to-the-23rd dept.

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.

8 of 63 comments (clear)

  1. Musical theme dictionary by judd · · Score: 3

    Yes, Ian Witten and Lloyd Smith at the University of Waikato built one where you can whistle, hum or sing into a Java applet and it would find matching themes. ISTR that it's actually the rhythm that most strongly identifies the theme - everyone can tell that dit-dit-dit-dah is beethoven's 5th Symphony, even stripped of all pitch info. Add contour, andf you're away. It's called Meldoex - Melody index.

    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&p =coltitle for a demo.

  2. Re:Thanks, Rob! by BridgeBum · · Score: 3

    Ah, fun with Pythagorian triplets.

    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. :)

    ----

    --
    My UID is the product of 2 primes.
  3. But it's badly broken! by kzinti · · Score: 4

    I tried giving the Encyclopedia the ISO-RR33 benchmark integer sequence 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

  4. I've used this... by bunyip · · Score: 4

    I've had occasion to use this and thought it was pretty cool. There have been printed versions of these, but the online one is better.

    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) := 1,2,1,1,1,1,1,1.....

    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 sure who did it.

    Alan.

  5. Thanks, Rob! by Marvin_OScribbley · · Score: 4

    Wow this has been a subject that nobody seems to want to say anything about.

    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) ;-)

    --
    I'm not a journalist, but I play one on slashdot
  6. If you were wondering... by niven · · Score: 4

    ID Number: A034826
    Sequence: 0,1,1,2,4,9,20,48,115,286,719,1841,4755,12410,3255 8,85849,226980,601373,1594870,4232100,11 230771,29798539,79034638,209526631,555172356,14701 95001,3891131705,10292857772
    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

    --
    It only hurts when you survive
  7. As long as we're talking about numbers... by nosaj · · Score: 5

    Another great resource is the Inverse Symbolic Calculator. 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."

  8. Get the book! by wabewalker · · Score: 5

    Encyclopedia of Integer Sequences by N.J. Sloane and S. Plouffe, USD$57. It is actually neat; I found it in a (university) library once. There is a fine line between "combinatorics" and "recreational mathematics" sometimes, and that's good. The book will certainly have a large number of sequences that you'll find interesting if you have any interest in mathematics whatsoever. Other sequences are horribly technical. It's a very useful book and not as boring as some of the previous posters think.

    --
    --- Premature complacency is the evil of all roots