Sum of consecutive integers problem

Which numbers can be written as a sum of (at least two) consecutive integers? For example, 30 = 9 + 10 + 11 and 31 = 15 + 16, but 32 cannot be expressed as a sum of consecutive integers.

In this week's table, show how to express each number as a sum of consecutive integers (or that it cannot be done). The ultimate problem is to determine for which numbers this expression is possible, and for which it is not. (Bonus problem: How can you tell in advance how many consecutive integers will be required, assuming that the number can be expressed as the sum of consecutive integers?)

So, once again, everyone fill in at least two rows of the following table. This should give us sufficient data to figure out a pattern and solve the problem for any n. Be sure to identify yourself as the author of your rows.

If you have any questions about this, or thoughts that might lead toward the general solution, be sure and post them to the threaded discussion.

As you complete the table, try to type the HTML code directly into the source file -- don't use an HTML composition program like FrontPage.

n Situation Author
1 Cannot be done Dr. D
2 Cannot be done Dr. D
3 1+2 Dr. D
4 Cannot be done Dr. D
5 2+3 Dr. D
6 1+2+3 Dr. D