The beauty of the palindromic sequence is that it is a sequence of a single integer. For example, the sequence A-B-A-B-A-B-A-B-A-B-A-B-A-B-A-B-A-B-A-B-A-B-A-B-A-B=23 is a palindromic sequence.
Another benefit of having a palindromic sequence is that you know how long the first three digits will be. So in this sequence, you know that the first two digits are 15 and the third is 13. You also know that the whole number is 23.
The reason I love palindromes is because of the ability to count them as an easy way to build up a long sequence of numbers. For example, if you have a sequence of 7s in a palindrome, you could count it as 7s, 9s, 11s, 13s, or 17s. You could also count each of the digits separately, as a palindrome, as 7s, 9s, 11s, 13s, or 17s.
The fact that some sequences of numbers can be counted as palindromes is a really cool property of our numbers, so the ability to count a palindrome and say, “Oh, that’s a palindrome.” can be very useful. But here’s the rub: The ability to count palindromes isn’t something you can do, like you can count a number as a different number.
Thats right, you cant.
This is a good place to start, as you get to the bottom of the question, “the first digit is 7.” The first digit is the letter A, then 7s, 9s, 11s, and then 1s, 1s, 2s, 3s, 4s, etc. There’s a reason that most of the digits are A-Z. For example, the letter A is A-Z (or A-Z, as it stands in the US).
So, if you can count a palindrome, than you can count the palindromic sequence of all 1’s. If you can count all the 1’s then you can count the palindromic sequence of all the A’s. If you can’t then you can find a palindromic sequence of all the A’s and A-Z’s. There are plenty of examples of this in the book.
The problem with counting palindromes is that it only works with whole numbers. If you want to count palindromes of all the numbers from 1 to 10, you can always count the palindromes of all the numbers from 1 to 11.
There are dozens of examples of this. We’ve seen this with our friends, our family, and our country. It’s one of the many reasons we put up a website called “Palindrome” so that we can show all the palindromic sequences of 1s, As, and A-Zs.
If you want to learn more, the website has a ton of stuff on it and a ton of cool palindromic sequences. You could also check out our article on palindromes.
