I'll hazard a guess with the attached. I used a helper column J and counted the contiguous periods in column K.
Columns E, F, G and H were there to help me find some kind of pattern.
BTW: the file had some dates that were text.
Edit: Both formulas are array formulas. They must be committed by simultaneously pressing Ctrl + Shift while hitting Enter. Then fill down. You'll know it is entered correctly when you see the {} curly braces around the formula. You don't type these in yourself. Excel does it for you.
Another BTW: That ugly formula in column J can be replaced by this.
Formula:
=IF(SUM(IFERROR(IF(IF($A4=$A4:$A$20,ROW(INDIRECT($C4&":"&MAX($C$4:$C$20))),"")=$C4:$C$20,1,""),""))=1,1,0)
It is array entered also.
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