Nikon d5100 saving pictures?

Lets say i take 100 pictures on my nikon d5100 the camera will save the pictures as dsc_0001 through dsc_0100 but when i delete the pictures and take pictures again the pictures are saved with the same name this happens all the time is this how its suppose to be or is there way to fix it

Added (1). Thanks everyone for your answers but Jeroen was right, turned out by default the camera number sequence was off so i went into the menus and turned it on

Yup, it numbers them in sequence and it's nothing to worry about.

There's a setting in your menus somewhere if it should continue numbering or reset if you insert a fresh card. I'd advice you to set it to continuous.

Best practice for any camera is to offload the entire card to the computer every month at least and format it in camera.

See page 162 in your manual.