Grabbing data in a worksheet and transposing in another... or something like that!

This is probably a very simple formula, but after doing my best with VLOOKUP, HLOOKUP and IF... I just can't figure it out! I have a spreadsheet with up to 10,000 rows in column A. Here is an example:
A
1 Case Number
2 123456
3
4 Name
5 Joe
6
7 Case Number
8 98765
9
10 Name
11 Bill
12
13 Case Number
14 112233

What I want to do is, in a new worksheet starting at cell A2 scan the above sheet and every time I find “Case Number” display the value underneath (even if it is blank). Then proceed to cell A3, find the next “Case Number” again and display the next value below. Like this:

A
1 Case Number
2 123456
3 98765
4 112233

The only other constraint I should mention is the number of rows between subsequent “Case Number”s on the first sheet is not always the same, so I can't use a formula that says “go down exactly 6 rows each time and grab those values”. Row distances between case numbers is effectively random at times.

Maybe I need a macro and not a formula? Any help would be greatly appreciated!

Wow that was fast, you guys RULE! You have saved me soooo much time! You are the BEST!!