Need to create different/patterned periods ordered by week

Hi, I need help creating a date range.

My company seperates the year into periods of 4 weeks starting at the beginning of the year, then the next 4 weeks, then the next 5 weeks,  this then repeats, 4  4  5. Is there a formula that can help me create a date range that allows me name the week number of each period? Say, week 1 of period 5?

Any help is very much appreciated!