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.