Two bits of inauguration math

It’s Martin Luther King Day and also the day of the presidential inauguration. (Which is an… interesting juxtaposition.) How often does this happen?

The relevant definitions are:

• MLK Day is the third Monday in January, every year. King was born on January 15, 1929, and certain US holidays always are made to fall on Mondays to give people long weekends. This has been the case since it was made a holiday in 1986.
• Presidential inaugurations are held on January 20, except in years when that is a Sunday, in which it is Monday, January 21. They take place every four years, in years one more than a multiple of four. This has been the case since 1937. Before that the president was inaugurated on March 4. I imagine the cold that is expected to affect today’s inauguration would be less of a problem then.

So the two have coincided on Monday, January 20, 1997 (Clinton’s second inauguration) and Monday, January 21, 2013 (Obama’s second). Given the 28-year cycle of the calendar in the short term, this continues:

2025, 2041, 2053, 2069, 2081, 2097

But that 28-year cycle relies on leap years coming every four years, and 2100 won’t be a leap year. So there will be irregularities around 2100 (and also 2200 and 2300). The full calendar follows a 400-year cycle, in which the coincidences are in the following years. Blue is years when MLK Day falls on January 20, red on January 21.

2013, 2025, 2041, 2053, 2069, 2081, 2097

2109, 2121, 2137, 2149, 2165, 2177, 2193

2205, 2217, 2233, 2245, 2261, 2273, 2289

2301, 2313, 2329, 2341, 2357, 2369, 2385, 2397

and every 400 years thereafter. Across century boundaries. you get a recurrence after 12 or 40 years (plus 2 or 9 leap years), as from 2097 to 2109. So in a full 400-year cycle, there are:

• 13 occurrences of Monday, January 20 in the year after a leap year, like today
• 16 occurrences of Monday, January 21 in the year after a leap year, like in 2013

so today’s coincidence happens 29 times out of 100, or very nearly two of seven.

Also, former president Jimmy Carter died on December 29, at age 100, after a surprisingly long period in hospice care (nearly two years!) . He wanted to make it long enough to vote for Kamala Harris, which he did on October 16 – his birthday was October 1. I like to think he did not want his funeral to take place under Trump. Flags fly at half-mast for thirty days after a president dies. So has a president ever been inaugurated in this period of mourning?

As a quick estimate, there have been 45 distinct presidents, but five (the younger Bush, Clinton, Obama, Biden , Trump) are still living, so there are 40 dead presidents. Therefore, if this has always been the law, there have been forty months of such mourning. Presidents are inaugurated every four years, so we’d expect something like 40/48 of these. (I am of course ignoring non-regularly-scheduled inaugurations caused by a president’s death – they don’t get a ceremony anyway.)

As it turns out, there was one. Harry Truman died on December 26, 1972, putting Nixon’s second inauguration, on January 20, 1973, within the period with flags at half mast.

Flags won’t be at half-mast today. in Washington and in many states, but will go back down after the inauguration. This is, as far as I can tell, because Trump is petty. There are two Georgians he doesn’t want to share his day with.