One graduate student's punched cards became a database of 390,000 sequences
In 1964 a graduate student named Neil Sloane began jotting down integer sequences he met in his research, storing them on punched cards. Six decades later the collection, now the On-Line Encyclopedia of Integer Sequences, holds more than 390,000 entries. Mathematicians type in a few numbers they have stumbled on and discover who met them first.
Sloane was working in combinatorics, where the same strings of numbers keep cropping up in unrelated problems. He published selections twice as books: A Handbook of Integer Sequences in 1973, with 2,372 entries, and a larger Encyclopedia in 1995 with Simon Plouffe, holding 5,488. Readers responded by mailing him more, and the flood outgrew print. At 16,000 entries he took it online, first as an email service in August 1994 and then as a website in 1996.
Each entry lists the opening terms, keywords, formulas, references and the reason anyone cared, and users can graph a sequence or even listen to it played as music. Every sequence carries a label of the letter A plus six digits. The primes, for instance, sit at A000040 and the Fibonacci numbers at A000045. Search works by keyword or by typing a run of terms, and a tool called SuperSeeker throws many algorithms at an input to guess what it might be.
Milestones get special treatment. The 100,000th entry, added in 2004, counts the notches on the Ishango bone, an ancient carved bone. For number 200,000 in 2011, editors spent a week debating which sequence deserved the round number, eventually moving one there from A200715. The database even includes self-referential oddities, such as a sequence whose terms are drawn from other sequences by their own index numbers, which Sloane admits he resisted for the sake of the database's dignity.
The encyclopedia stretches its remit by turning other objects into integers. Fractions become paired sequences of numerators and denominators, and pi appears as its decimal digits, its binary digits and its continued fraction. Sloane moved the work to a foundation in 2009 and chairs it, and volunteer editors have shared the load since 2002. It still grows by roughly 30 sequences a day.
Source: On-Line Encyclopedia of Integer Sequences
