Python code that finds the number of palindromes

Question

I am very confused, I do not know what kind of equation I should make. I cannot think of anything other than 1 that satisfies this condition. Can you give me some guidance on how to write this code?

For example, let me enter 3 as the number n. From ((2 ^ n) -1) comes = 7. I need to find a 7-digit palindrome number like 1670761

Answer 1

This code should work:

def len_x_palimdrome(x,f,start = ""):
    #f - a callable object taking one input and returning a bool
    nums = "0123456789"
    for i in nums:
        if x == 1:
            if f(int(start+i+start)):
                return(i)
        elif x == 2:
            if f(int(start+i*2+start)):
                return(i*2)
        else:
            a = len_x_palimdrome(x-2,f)
            if a != None:
                return(i+a+i)
    return(None)

The function takes in the length and a function lambda or whatever that will be used as a filter. Note that the function will return the lowest palindrome that fulfills the requirement(s) defined in the function.

Example filter function:

def f(n):
    if n == 0:
        return False
    return n%7 == 0

In conclusion:

print(len_x_palimdrome(2**3-1,f))