Ask HN: How do I think about recursion in math and programming?

I got the idea for problems like factorials or finding sum from 1 to n, where there's a pattern visible. Like this:

Source:https://99x.io/blog/recursion-is-not-hard-here-is-the-right-way-to-think

I got it for things like addition, subtraction, division, multiplication of two numbers as well.

eg: a+b

=a+b-1+1

=SUM(a+1,b-1)

Now, I am wondering how it'll be for finding a palindrome of a number? I've a solution but I'm not understanding how we came towards it. I'm looking for how to come towards a solution than a solution itself.