1955 Birthdays

For everyone who was born in the last ten months of 1955, in each of the subsequent years ending in a double digit, our birthdays fall back on the same day of the week as our original day of birth in 1955.

For example, I was born on a Wednesday in '55, and my birthday fell on on a Wednesday in each double-digit year since ('66, '77 and '88). Moreover, it will continue to do so for most of my expected life (in '11, '22, '33 and '44). The triple-digit years (1999 and 2000), of course, do not count.

Explanation

The calendar for a non-leap-year normally repeats itself after 6 and 11 years. Having been born between March and December of 1955, less than a year to the next leap day, my first calendar repeated itself three times -- in 1966, 1977 and 1988 (plus a few other years in between).

Normally, 1988 being a leap-year, this would have been the end of the sequence, but by a combination of events (the juxtaposition of 1999 and 2000, with the latter indeed being a Gregorian leap-year), the sequence was knocked back on course for another batch of four events (2011, 2022, 2033 and 2044). The property will therefore fail for the first time on my 100th birthday, in 2055.

Because of its reliance on excluding triple-digit years, this property only holds for those born between March and December 1955, and for those in no other years since 955 (using the Julian calendar), or again until 3955 (using the Gregorian calendar).

Calculating the day of the week

Meanwhile, here is an algorithm for calculating the day of the week for any given DD-MM-CCYY (where CC is the century).

Treat January and February as months 13 and 14 of the previous year
Calculate the offset for the century: 5*CC+CC/4 (integer division)
Calculate the offset for the year: 1*YY+YY/4 (integer division)
Calculate the offset for the month: case(MM){0,3,2,5, 0,3,5,1, 4,6,2,4, 0,3}
Calculate the offset for the day of the month: 1*DD
Add all of the offsets together, and find the remainder when dividing by 7

Example-1, 26-Oct-1955 gives MOD( 5*19+19/4+55+55/4+6+26, 7) = MOD( 199, 7) = 3 = Wednesday
Example-2, 14-Feb-2017 gives MOD( 5*20+20/4+16+16/4+3+14, 7) = MOD( 142, 7) = 2 = Tuesday

Where appropriate, 5*CC can optionally be handled as -2*CC.