The On-line Encyclopedia of Integer Sequences, or, Confessions of a Sequence Addict: An MAA Invited Address by Neil J. A. Sloane, AT&T Shannon Labs

Here are the first three terms of a sequence: 1,16, 29568. What does this sequence represent? What is the next term? (Answers: It equals the number of ways to arrange 1, 2, 3, n2 in an n x n square so that there is only one local minimum, given that the only neighbors of a cell are horizontal and vertical to that cell. The next term is 35704394880.) Other than being given the answer, how could you possibly know this?

One way is to search in "The On-Line Encyclopedia of Integer Sequences," which currently contains 91,000 sequences--up from 10,000 eight years ago--including the one above. The speaker, Neil Sloane--also the founder and maintainer of the website--began collecting sequences in 1963, and has not stopped since. The "Handbook of Integer Sequences," published in 1973, was followed by "The Encyclopedia of Integer Sequences" in 1995, and the website was up and running the following year.

Sloane followed with more facts about the website. For example, the website gets about 30,000 "hits" per day--about 10,000,000 hits per year. It also receives about 40 new sequences per day or 12,000 per year. The database functions not only as a kind of dictionary of sequences for those in the fields of enumeration, number theory, game theory, physics, chemistry, computer science, etc., but as a gateway for the "person on the street" and around the world to start doing mathematics.

Of course, the presentation would not have been complete without some examples of sequences offered to the audience for our enjoyment. Example: given the puzzle sequence: 71, 42, 12, 83, 54, what number comes next? (Hint: move the commas one place to the left, and the numbers are all multiples of what small prime number?) We played with Eban Numbers, Home Primes, approximate squaring, and Dismal Arithmetic (not at all, really).

As far as the future of the website is concerned, this "public good" may eventually find a new home separate from the AT&T website. Meanwhile, for more information (and a good time), go to The On-Line Encyclopedia of Integer Sequences.

Happy hunting!

-- Claudia Clark, AMS-AAAS Media Fellow

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