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Pentax K body + Nikon F lens

PARTIALLY COMPATIBLE

The flange focal depth should allow conversion, but...

The difference in flange focal depth in only 1.04 mm in favor of the F. This means that even if conversion is possible, you'll have to live with compromises due to the extra lens in the system.

Keep in mind that using a fullframe F lens will get you a crop factor of 1.6*, because of the APS-C sensor of the Pentax K body, you'll get a pretty high focal length multiplier (you'll get a smaller image frame). Find out more about focal length in this article if you're interested.

Don't forget that aperture control won't be available for every Nikon F version (there's a multitude of them, check out the different versions here).


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Terminology

In terms of compatibility, we distinguish four separate categories:

COMPATIBLE
PARTIALLY COMPATIBLE
COMPATIBLE IN THEORY
NOT COMPATIBLE
This means that you'll be able to apply the lens on the camera in question with a proper adapter, and full focus range will be available with it (often with aperture control too). If AF is supported, you'll see it in the description.
This means that due to the flange focal depth or other factor this conversion would be normally unfeasible, but with some compromises (e.g. using a speedbooster adapter) can be made possible.
This means that the flange focal depth should make mounting and using inifinty focus possible, but for some reason there are no adapter rings available or other factors make it unviable.
This means that you won't be able to mount your lens due to mechanical incompatibility or the difference in flange focal depth doesn't make inifinity focus possible. Although numerous lenses can be mounted on cameras without infinity focus, but this cannot be considered actual compatibility.

Additional information for compatible variations:

MF
AF
MA
AA
SB
MAC
TS
manual focus (on the lens, with its own control ring)
autofocus available (AF controlled by the camera body)
manual aperture control (on the lens, with its own control ring)
automatic aperture control (controlled by the camera body)
speedbooster (focal reducer) adapters are available
macro (variable length) adapters are available
tilt-shift (or other flexible) adapters can be used

If you'd like to read more in-depth about compatiblity, you'll need to get familiar with flange focal depth, see this article.