
Calendar formula for 2nd Wednesday of each successive month
Posted:
Jan 24, 2013 11:51 PM


The last time I wrote about a calendar curiosity was when I asked how many calendar years do I need in order to not have to buy a new calendar. And the answer is 7, if we ignore leap years. The answer is 7 because I need only 7 calendars that start the january 1st with one of the seven days of the week. If I have those, I need not buy any new calendar.
But now I have a new calendar question, sort of a reversal of the 7 calendars. I am receiving social security checks every 2nd wednesday of the month. So the question is, what math formula can be written that tells me how many days in each month, starting January of 2013 for the next ten years, how many days in each month that I have to wait for the check.
For example, January 2013, the first wednesday was 2nd and the second wednesday was the 9th which means I had to wait 9 days for Jan 2012 to receive the check. Now Feb 2012, the first wednesday is 6th and the second wednesday is the 13th so I have to wait 13 days.
So far I have this: 2013 Jan wait 9 Feb wait 13 . . .
So what is the formula that gives me those numbers without consulting a calendar? Here I would have to include leap years.
And it is obvious that the numbers have a lower limit of 7 and a upper limit of 15, depending on what day is the first day of that month.
What I am interested in is whether there is a internal pattern that can easily tell me if a month is going to have a early payday or whether it is near to 15 day wait.
And I wonder if some years are going to have many 7 day paydays or many 15 day paydays, given that a probability of a 7 or 15 day month is about 1 per year since we have 12/7 = 1.7
Anyone figure out a formula?
And I would guess that there is a general formula for what day is the 1st of the month for the next ten years has been figured out and that this formula is part of the solution for the 2nd wednesday of each month.

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