I have an exercise in which I am require to build a recursive function that takes a natural number and returns True if it is divisible by 3, or False otherwise, using the 3-divisibility rule. Then I was asked to write a recurrence relation of this function. The function I wrote is:def divide3(n):    i=0    while i in range(0,len(str(n))-1):        if (sum(n, i))%3==0:            if (divide3(int(str(n)[i+1:])))==True:                return True            else:                return False        continueWhat I don't understand is how I am supposed to write an n-depended recurrence relation, if the number of operations I make is related to the number of digits in n, and has nothing to do with n itself. I would appreciate any help in the subject. 
How to write a suitable recurrence relation for a python function?
python
Sorry, but your code doesn't work at all and makes no sense whatsoever. If it gets into the loop at all, it immediately gets killed by an error. Did you even try it? I'd recommend first getting it right instead of trying to come up with a recurrence relation for something broken. Or did they ask you for the recurrence relation because they saw your code and also had no idea what you were doing, so this is their way of trying to get you to explain?What's the 3-divisibility rule? You mean that a number is divisible by 3 if and only if its digit sum is? If so, then that directly tells you what to do: When asked whether some number is divisible by 3 and you don't know right away, ask yourself whether its digit sum is divisible by 3. If that number is still too large to see it directly, ask yourself whether the digit sum of that number is divisible by 3. And so on.Straight-forward implementation then: def divide3(n): return n in (0, 3, 6, 9) if n < 10 else divide3(sum(map(int, str(n))))Bit more interesting: def divide3(n): return n in (0, 3, 6, 9) if n < 10 else divide3(n//10 + n%10)(Sorry about the formatting, don't know how to spoilerize code.)