So my friend made a comment that the problem with number patterns is that you can make them arbitrarily difficult...well, these get pretty difficult, although not too complex (i.e., the algorithms are short, but may be hard to find!).
Find the next numbers and the algorithm for the following:
Easy:
1,3,7,15,31,63,127,255,511,1023,2047
Normal:
1,2,4,13,77,702,8478,126127,2223279,45270000
Heroic:
1,5,14,24,59,92,183,217,274,389,708,801,1282,1569,1784
Legendary:
3,-1,-6,30,23,87,78,178,-1153,-1165,-3362,-3166,-3181
GAME OVER....Do you wish to continue? ;P