Renaming files by date taken adding increment with skip

Is it possible to provide a new file name for images based on: 1) the date the image was taken and 2) numbering restarting with each date change and skipping at a predetermined interval?

Here's an example of the proposed renaming:

Current File Name Date Taken Proposed Name
Scan 81.jpeg 9/12/1930 8:15 AM 19300912 001.jpeg
Scan 58.jpeg 9/12/1930 1:31 PM 19300912 003.jpeg
Scan 60.jpeg 9/12/1930 1:31 PM 19300912 005.jpeg
Scan 5.jpeg 9/12/1933 7:02 AM 19330912 001.jpeg
Scan 4.jpeg 9/12/1933 7:03 AM 19330912 003.jpeg
Scan 6.jpeg 9/12/1933 7:03 AM 19330912 005.jpeg
20210910 Scan 3.jpeg 9/12/1936 7:05 AM 19360912 001.jpeg
20210910 Scan 32.jpeg 9/12/1936 7:09 AM 19360912 003.jpeg