Problem with Week Numbers between dates on New Year - excel

Question

Problem
The following [mcve] will output an array of arrays of week numbers between two dates. It works when both dates are on the same year, however, some years have 52 weeks and start within the last days of the last year. And others have 53 weeks.
An example of 52 weeks is the 2020 calendar:
Where the first week begins on Dec 30.
And the example of 53 weeks is the 2016 calendar:
That begins only on Jan 4th.
Code
The following code is commented and outputs an array of arrays with the week numbers.
Sub w_test()
Dim Arr() As Variant, ArrDateW() As Variant
'Initial Date
DateI = DateSerial(2015, 5, 5)
'Final Date
DateF = DateSerial(2017, 9, 20)
'Difference in weeks between DateI and DateF
weekDif = DateDiff("ww", DateI, DateF) + k - 1
i = Weekday(DateI)
d = DateI
'If not Sunday, go back to last week, to start the loop
If i <> 1 Then
d = DateAdd("d", -(i - 1), d)
End If
ReDim ArrDateW(weekDif)
ReDim Arr(2)
'Loop on all weeks between two dates to populate array of arrays
For i = 0 To weekDif
'Date
Arr(0) = d
'Trying to solve problem with New Year
If Application.WorksheetFunction.WeekNum(d) = 53 Then
flag = True
End If
If flag = False Then
Arr(1) = Application.WorksheetFunction.WeekNum(d)
Else
Arr(1) = Application.WorksheetFunction.WeekNum(DateSerial(Year(d) + 1, 1, 1))
flag = False
End If
'Year
Arr(2) = Year(d)
'Populate array of arrays
ArrDateW(i) = Arr
'Next Week Number
d = DateAdd("ww", 1, d)
Next i
'To stop with Ctrl+F8
Debug.Print d
End Sub
Question
2015 had 53 weeks, however the program outputs the following:
And between 2016 and 2017, the output is a mess:
How to fix the program to output these week numbers correctly?

Answer 1

I went about it somewhat differently, relying on built-in VBA functions to correctly calculate the week numbers. Read about ISO week numbers is this answer and see how I'm using the DataPart function -- though you can substitute your own version of Ron de Bruin's ISO week number function if you feel it's warranted.
A couple of quick side notes:
Always use Option Explicit
Try to use more descriptive variable names. YOU know what you're talking about NOW. In a few months, you'll struggle to remember what d and Arr mean (even if it seems obvious now). It's just a good habit and makes the code self-documenting.
My example below breaks the logic into a separate function with an optional parameter (just for fun) that would allow the caller to change the start of the week to a different day.
Code module:
Option Explicit
Sub w_test()
Dim initialDate As Date
Dim finaldate As Date
initialDate = #5/5/2015#
finaldate = #9/29/2017#
Dim weeks As Variant
weeks = WeekNumbers(initialDate, finaldate)
Debug.Print "There are " & UBound(weeks, 1) & " weeks between " & _
Format(initialDate, "dd-mmm-yyyy") & " and " & _
Format(finaldate, "dd-mmm-yyyy")
End Sub
Private Function WeekNumbers(ByVal initialDate As Date, _
ByVal finaldate As Date, _
Optional ByVal weekStart As VbDayOfWeek = vbSunday) As Variant
Dim numberOfWeeks As Long
numberOfWeeks = DateDiff("ww", initialDate, finaldate, weekStart, vbFirstFullWeek)
Dim startOfWeek As Date
If Weekday(initialDate) <> vbSunday Then
Dim adjustBy As Long
If Weekday(initialDate) > weekStart Then
adjustBy = Weekday(initialDate) - weekStart
Else
adjustBy = (Weekday(initialDate) + 7) - weekStart
End If
startOfWeek = DateAdd("d", -adjustBy, initialDate)
End If
Dim allTheWeeks As Variant
ReDim allTheWeeks(1 To numberOfWeeks)
Dim weekInfo As Variant
ReDim weekInfo(1 To 3)
Dim i As Long
For i = 1 To numberOfWeeks
weekInfo(1) = startOfWeek
weekInfo(2) = DatePart("ww", startOfWeek, weekStart, vbFirstFourDays)
weekInfo(3) = Year(startOfWeek)
allTheWeeks(i) = weekInfo
startOfWeek = DateAdd("ww", 1, startOfWeek)
Next i
WeekNumbers = allTheWeeks
End Function