Recreating an RNG in Python

I am trying to recreate a multiplicative congruential algorithm that is used in Matlab (Found it here, section 9.2, read it for a little context)

Basically, I have 4 variables

a = 13
c = 0
m = 31

And this last one, which I can't format to code because it breaks the subscript:

x₀= 1

And with those four, I'd like to reproduce something like this :

x_k+1 = a * x_k + c mod m

So far, I've got :

a = 13
c = 0
m = 31
base = 2 # Does not work with 0 for some reason
x = int(x='1', base=base)

for i in range(8):
    rand = a * x + c % m
    base += 1
    x = int(x='1', base=base)  
    print(rand)

And my output is :

13, 13, 13, 13, 13, 13, 13, 13...

Even though, according to the document, should be :

1, 13, 14, 27, 10, 6, 16, 22...

So I'm not sure if I completely misunderstood the question, or if what I'm trying to accomplish is simply not possible in Python, or if I'm just going bonkers, but I desperately need some advice. Any insights are greatly appreciated.