To expand on my comment above, you can do this by hand by picking a non-primary color that you like for the end pieces, and reverse engineer what colors might be used to get that result.
I tried this with a violet color and a teal color, and came up with the following results:
The key will be to pick something that is not Red, Yellow or Blue for your end color.
If mixing colors in your head doesn't come naturally to you, here's an online mixing tool that might help: http://trycolors.com/. It lets you mix colors to see the results, and also has a pallet of pre-mixed colors that you can expand to see what colors it's made of. This won't help with reverse engineering, but it might be helpful to play with to see if your final result makes sense.