I am creating a flat database to catalogue my Microscope slides, and using the serial number function to automatically number the slides. If I remove a slide from the collection, how can Filemaker pick up that there is a gap in the sequence and offer to fill that gap when the next entry is created.

It doesn't do that and it not a good idea to try to fill the gaps.

As you will see I am fairly new to FM, to help could you please give the reasoning behind your reply...

many thanks

If you really want to fill the gaps, don't delete the records. Use a script to remove the data. Now when you want to add data, do a find for records that have one or more empty fields. Go to one of these records and add the new data.

To find an empty field use the = by itself as the find criteria.

Ok... many thanks for the reply