You may want to read (or you may not want to !) this:

http://naca.larc.nasa.gov/reports/1929/naca-report-295/

It's a very old NACA report. I think that IC engines still operate in the same manner back then as they do today though. Specifically, in the conclusion section, on page 10, they show a BHP ratio of about .70 at 10k feet (in table 1), with BHP reduction almost linear in our altitude regime.

Density of air at 10kft = 89% of sea level density, assuming STP. So propeller thrust should go down accordingly, given the same 6000 rpm.

I only gleaned over the report, but what I got was yes, the propeller would be putting out less thrust according to density change. Engine power output would be much less than 89% though. Without looking much at the numbers, I would predict RPMs would still go down from your 6000 rpm at sea level.

I guess thats why superchargers are used for much higher operations. Maybe I'll actually read the report later!