The Connoisseur of Number Sequences


Erica Klarreich in Quanta Magazine:

Neil Sloane is considered by some to be one of the most influential mathematicians of our time.

That’s not because of any particular theorem the 75-year-old Welsh native has proved, though over the course of a more than 40-year research career at Bell Labs (later AT&T Labs) he won numerous awards for papers in the fields of combinatorics, coding theory, optics and statistics. Rather, it’s because of the creation for which he’s most famous: the Online Encyclopedia of Integer Sequences (OEIS), often simply called “Sloane” by its users.

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 arrangen 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.

A mathematician whose research generates a sequence of numbers can turn to the OEIS to discover other contexts in which the sequence arises and any papers that discuss it. The repository has spawned countless mathematical discoveries and has been cited more than 4,000 times.

“Many mathematical articles explicitly mention how they were inspired by OEIS, but for each one that does, there are at least ten who do not mention it, not necessarily out of malice, but because they take it for granted,” wrote Doron Zeilberger, a mathematician at Rutgers University.

The collection, which began in 1964 as a stack of handwritten index cards, gave rise to a 1973 book containing 2,372 sequences, and then a 1995 book, co-authored with mathematician Simon Plouffe, containing just over 5,000 sequences. By the following year, so many people had submitted sequences to Sloane that the collection nearly doubled in size, so he moved it onto the Internet. Since then, Sloane has personally created entries for more than 170,000 sequences.

More here.