New Year’s Day is one of my favorite holidays, second only to Thanksgiving. Even though the timing is arbitrary (it falls well after the winter solstice and a few days before perihelion) and nothing substantial really changes in my life from those few minutes before midnight until a few minutes after, I like the idea of getting a somewhat clean slate and a fresh start.

After the train wreck that was 2020 and the “not much better” that was 2021, I am cautiously optimistic about 2022. I’m going forward without resolutions except trying to become a better person, but I am trying to do that all of the time. But I am refraining from statements like “2022 is gonna be great!” etc. For example, where I live the high temperature today was 78.4F (nearly 26C) which is not what I expect on the first day of January. Is that just a nice day or the harbinger of something worse?

For me the main thing about 2022 is that it is the first year I’ve ever experienced that contained three 2s. It made me think about how often that has happened, and it turns out this is just the third time.

The first “three 2” year was 222, of course, and it took a thousand years before 1222 became the second year. Now eight hundred years have passed since then to get us to 2022.

The next one is a rather rapid one hundred years away to 2122, then eighty years to 2202 and then it is just eighteen years to 2220, which will start a ten year run of “three 2” years.

I kept trying to figure out if there was a pattern:

1000, 800, 100, 80, 18

and perhaps there is some sort of mathematical series that defines when these numbers with duplicate digits appear, but I haven’t been able to find one.

For example, for “three 1” years you get 111 followed nine hundred years later by 1011 followed ninety years later by 1101, followed nine years later by 1110, which starts its ten year run:

900, 90, 9

Seems like there should be some way to express this but I’m not seeing it. Note that if you multiply these numbers by 2 you get 1800, 180 and 18, which looks familiar (grin)

So there you are: my gift to you for 2022. Figure out if there is a way to express the distance between numbers with duplicate digits, and any case I hope that 2022 is a great year for you and yours.