From an overview perspective, it makes sense to pick those specific numbers.
The only other option would be 2/4/6, but then people might get confused with it representing core count. You wouldn't want to really use 1, except as a backup number, plus you could argue that Celeron is 1 and Pentium is 2, meaning that 3 is the lowest reasonable marketing and logical number.
If you're using 3, you don't want to use 4 for two reasons, because you want the option of adding another series if you decide to restructure, adding products between the current ones (when it's established that the unmbers don't refer to core or thread counts) and also you can add an i9 series, so you move up by two, giving 5.
If you have three products, then 3/5/7 makes most sense. Gives you option to expand upwards, while not confusing model numbers with core counts, and prevents people thinking they are getting the very lowest "1" model.
When you consider that these families extend to mobile as well, you can't use thread counts because the i3 has 4 threads, so making an 8 thread core an i8 and a 2 core, 4 thread core an i2 would be confusing. The mobile chips also don't share the same characteristics as the desktop chips.
Then there are the 6 core i7 chips for 1366/2011 sockets, which would also break the pattern.