1. Define a function that takes a positive integer and returns the sum of its digits. Two mathematical operations that might be useful here are modulo and division. You get 2pts bonus credit if you solve the problem using proc_seq.

    Save the definition of proc_seq from here in a file named repo.py in the same directory as the code you write for solving the problem. Now, you can have proc_seq available for use by importing it from repo, by from repo import proc_seq. Here is the solution with proc_seq:

     from repo import proc_seq

 def sum_digits(n):
     """Return the sum of the digits of n in decimal representation.

     >>> sum_digits(0)
     0
     >>> sum_digits(123)
     6
     >>> sum_digits(4096)
     19
     """
     def sequencer(n): return n // 10
     def alive(n): return n > 0
     def update(state, n): return state + (n % 10)
     return proc_seq(n, sequencer, alive, update, 0)

  2. [3pts] You are asked to define a function to compute the sum of all the even numbers in the Collatz sequence seeded by $n$. You are asked to use proc_seq. Assume you have the collatz function defined. Write the update function you would pass to proc_seq as parameter.

    Add the collatz function to your repo.py.

     from repo import proc_seq, collatz

 def sum_even_collatz(n):
     """Return the sum of the even numbers in the Collatz sequence seeded by n.

     >>> sum_even_collatz(8)
     14
     >>> sum_even_collatz(3)
     40
     """
     def sequencer(n): return collatz(n)
     def alive(n): return n != 1
     def update(state, n):
         if n % 2 == 0:
             return state + n
         else:
             return state
     return proc_seq(n, sequencer, alive, update, 0)