A few months ago I took my then new camera (Nikon D7200) out with a tripod to take some small aperture shots. I noticed a significant amount of artifacts on the resulting pictures. A quick Google search informed me that this was sensor dust and to be expected at these apertures. My camera only had 1600 shutter actuations when I first noticed the spots and both the lenses I used were new. Below are two examples of pictures with the spots. The spots are easiest to see against the sky, but you may have to zoom in to see them. The spots are nonexistent when using apertures larger than about f/18. Is this normal for a DSLR, even when new? Is there a way to prevent/minimize these artifacts at small apertures without post-processing?
First image: f/36, 1 second, 140mm (first lens)
Second image: f/22, 30 second, 32mm (second lens + variable ND filter)