The recent thread about Palindrome/RADAR notes got me wondering what the relative frequencies of special serial numbers are.

I decided to write a little computer program to help answer my question and I thoughts others might be interested in the results too.
I was primarily interested in 7-digit palindromes (e.g. 1010101) since that was the number of digits in the $20 bill presented. I have some results that are relevant to RADAR note frequency (scarcity). The following points are true for serial number ranges such as AAA0000000 to AAA9999999:
- There are only 10,000 RADARs (including 0000000) or 0.1 % for a given 3-letter prefix. This means the odds of finding any RADAR note (for a given 3-letter prefix) is 1 in 1000.
- Rarity of RADAR increases with the number of unique repeating digits. The rarest is a palindrome of only one unique repeating digit, (a Solid, e.g. 1111111). The odds of finding a Solid for a given 3-letter prefix is 1 in a million (literally).
- Next is a 2-digit palindrome (e.g. 1010101). There are 270 2-digit RADARs. Similarly, there are 2430 3-digit RADARs (e.g. 1232321) and 7290 4-digit RADARs (e.g. 1357531). The sum of these four types (10+270+2430+7290) = 10,000.
In summary, for 7-digit serial numbers (including 0000000):
Overall RADAR odds: 1:1,000
4-digit RADAR oods: 1:1,372
3-digit RADAR odds: 1:4,115
2-digit RADAR odds: 1:37,037
Solid RADAR odds: 1:1,000,000
