Yes—this is normal for your lens. The Nikon 18-105mm is a variable-aperture zoom, marked 18-105mm f/3.5-5.6. That means its widest possible aperture is f/3.5 at 18mm, but as you zoom in, the maximum available aperture becomes smaller, reaching f/5.6 at 105mm.

An f-number is based on focal length divided by the diameter of the entrance pupil. As focal length increases, keeping the same f-number would require a larger effective opening. On a variable-aperture zoom, the lens cannot maintain that larger opening across the whole zoom range, so the maximum aperture decreases as you zoom.

That’s why if you set f/3.5, the camera raises it automatically when you zoom longer. But if you set f/5.6 or any smaller aperture (like f/8), that setting is available at all focal lengths, so it doesn’t change.

If you want the maximum aperture to stay constant while zooming, you need a constant-aperture zoom lens, such as one labeled f/2.8 or f/4 throughout the range.