Today on my way to work, I happened to notice that my mileage hit 18081 – a nice palindrome. I began to think – this seems to happen almost every one hundred miles or so. For example, my next palindrome will be 18281 followed by 18381, 18481, etc. There are hiccups when you switch to the 19000 mile range, so now instead of 19081 [which would be 100 miles from 18981], the next palindromal mileage mark is at 19091, or 110 miles later.There will be another skip at 19991 miles, which will be 20002, or 11 miles…
In an earlier phase, palindromes are easier to hit. For example, starting with 1 [by definition a palindrome, but a very boring one…] you get 2,3,4, etc. which are 1 apart. The next big leap, then is 11, which is 2 from 9 [not sure how this fits into the pattern yet…]. From 11, we have 22, 33, 44, etc. which are 11 apart. The next change in distance, then is 101, which is, strange enough, 2 from 99. The next series is 10 apart: 111, 121, etc. Then from 191 to 202 is again 11 apart. Moving from 999 to 1001 is only 2 steps [there’s that 2 again], but the next sequence is 110 apart: 1111, 1221, 1331, etc growing from 1991 to 2002 by stepping 11 [yet again].
So: adding a digit means you skip either 2 or 11 depending on whether or not the number of digits is odd or even – going from odd, you skip 2 and from even, 11. So, from 99999 to 100001 is only 2 apart. Nice, eh?
Okay – I know: enough already.
I love playing with numbers in my head – besides, it gives me something to think about while I ride since I can’t listen to the radio or anything. I wonder if I’ll ever hit 100001… Probobly not on this bike. In the car, definitely.