Database of integer sequences, both interesting and uninteresting, created and maintained by Neil J. A. Sloane of the AT&T Shannon Laboratory.  The web site is http://www.research.att.com/~njas/sequences/.

Typically, someone uses trial and error to calculate a few terms of a larger sequence.  For example, someone  discovers that he can solve the Tower of Hanoi problem in 1 move for 1 disk, 3 moves for 2 disks, 7 moves for 3 disks, and 15 moves for 4 disks.  He doesn't get the underlying pattern for some reason, and he goes to the Encyclopedia to look it up.  The encyclopedia presents some sequences with 1,3,7,15 in the middle, but the first one that he recognizes is the sequence {2^n-1}.  Looking around the site, he sees a number of sequences related to the Tower of Hanoi problem, and does further research from there.

Sometimes someone calculates a sequence, looks it up, and finds that the sequence also appears in a completely different area of mathematics.  Such serendipity leads to interesting work.

There are also some ringers.  Can anyone guess the origin of:

14, 18, 23, 28, 34, 42, 50, 59, 66, 72, 79, 86, 96, 103, 110, 116, 125, 137, 145, 157, 168, 181, 191, 207, 215, 225, 231, 238, 242 -- Sequence A000053.

-- EricJablow

''Interesting, I would never have guessed it was [CENSORED]. -- GarryHamilton''

Now that's useful information.  :-/   -- jtg

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CategoryMath / CategoryExternalLink