This is something I've been working with, and finally had the time to write up. The paradiddle shift is a pretty common exercise involving the displacement of the paradiddle by one 16th note. Most people get it through Stone's Stick Control; I first started using it after seeing it in a Modern Drummer article featuring Fred Sanford, in the early 80's. Usually it follows the sequence from Stone (p.5, ex. 5-8), with the paradiddle starting on the beat, then the 'a', then the '&', then the 'e'.
What I've done here is make the shift by adding a 16th note on the bass drum, which makes the displacements happen in reverse order. The order is not a big deal, the means of making the shift is:
Get the pdf.
YouTube clip with Fred Sanford's version of the paradiddle shift after the break:
Paradiddle exercise starts at 2:30: