“A Handbook of Integer Sequences” Fifty Years Later

New paper by N. J. A. Sloane.

Abstract: Until 1973 there was no database of integer sequences. Someone coming across the sequence 1, 2, 4, 9, 21, 51, 127, . . . would have had no way of discovering that it had been studied since 1870 (today these are called the Motzkin numbers, and form entry A001006 in the database). Everything changed in 1973 with the publication of A Handbook of Integer Sequences, which listed 2372 entries. This report describes the fifty-year evolution of the database from the Handbook to its present form as The On-Line Encyclopedia of Integer Sequences (or OEIS), which contains 360,000 entries, receives a million visits a day, and has been cited 10,000 times, often with a comment saying β€œdiscovered thanks to the OEIS”.

I’m proud to have a couple of sequences in OEIS:

  • A140961 (2008, with thanks to Vladeta Jovovic, whom I found viaΒ A051588, for the interpretation in terms of binary matrices). This arose when I was counting finite models of categorical syllogisms, thinking this might be useful for the psychology of reasoning. It wasn’t.
  • A358693 (1 Jan 2023) – whilst looking for properties of the number 2023. Trivial extension of A001102.