what sequences most need extending?

[Ed Pegg Jr]

My own personal favorite for extending is:

ID Number: A081287
URL:       http://www.research.att.com/projects/OEIS?Anum=A081287
Sequence:  0,1,1,5,5,8,14,6,15,20,7,17,17,20,25,16,9,30,21,20,33
Name:      Excess area when consecutive squares of size 1 to n are 
packed into the smallest possible rectangle.
References R. M. Kurchan (editor), Puzzle Fun, Number 18 (December 
1997), pp. 9-10.
Links:     Ed Pegg Jr, Packing squares
   http://www.maa.org/editorial/mathgames/mathgames_12_01_03.html
See also:  Cf. A038666.

Does it ever go back down to zero?  I'll pay $100 for a solution
to that.

The best known solution for 1-24 is
   http://www.mathpuzzle.com/24sqB.gif

Ed Pegg Jr