I have been in a position (for which I'm super grateful) in which young startups didn't have the funds to pay me my full-time rate, and so instead chose to pay me a weekly rate to work one week out of the month. I like to believe that I provided substantial value in that configuration - usually landing to review code, mentor newer programmers, and help chart direction for the subsequent three weeks (during which I'd be absent).
In this case, I was being paid quite a bit more than the full-timers, not less.
In time, they grew to be able to afford a more complete full-time cadre, and they people I worked with weren't so junior anymore.
I did this... I think half a dozen times. It was a great work config for everybody. If you can afford to travel to the work and you can really bring the fight for 5-8 straight days, I highly suggest it.