Some real ones from TopCoder in my experience (SRM 401, Div 1): http://apps.topcoder.com/forums/?module=Thread&threadID=6126...

(SRM 363, HandShake problem): http://apps.topcoder.com/forums/?module=Thread&threadID=5843...

The idea is you brute force or hand calculate the first few numbers and then use the OEIS's wild card search.

I've used it often to solve IBM's Ponder This puzzles. A dirty way to solve a puzzle is often to get a few values manually. These often are fractions, so there is a bit of an art in adjusting numerator and denominator so that the numerator sequence and denominator sequence both look somewhat regular. Then you look up those sequences in OEIS.

Well, the last time it helped me was as a "reverse lookup" for math knowledge I never got the "right" way through education.

For example, one of the Google-Foobar puzzles involves how many ways you can order a line of different-height elements so that only a certain number are "visible" if you stood at one end of the line or the other.

First I tried to figure out how I would solve it for small numbers by hand, creating a spreadsheet of inputs. At one point, I got a grid of numbers where the "simpler" rows/columns had a sequence like 1, 1, 1, 2, 3, 1, 6, 11, 6, which, through random googling and OEIS turned out to be "Unsigned Stirling numbers of the first kind"

http://oeis.org/A008275 https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_...

Alas, I'm still no math-major... the comments in my solution contain: "I'm extremely proud of this boiled-down end-result... except that I'm not sure I can fully explain why it works."