CS 115 Lab 6, Part A: Basic while loops: the Collatz sequence

The Big Picture

You will begin with a program that asks the user to enter a sequence of values and tells the user if each value is even or odd.

You will then modify this program to automatically generate the terms of a famous numerical sequence.

Background

The Collatz sequence works as follows.

You start by choosing a positive integer N. Then:

If N is 1, stop.
Otherwise, based on the value of N, generate the next term:
- If N is odd, the next term is 3N+1.
- If N is even, the next term is N / 2.
Repeat with the new value of N.

Here is an example, where the initial value of N is 6:

6, 3, 10, 5, 16, 8, 4, 2, 1

Make sure you understand how this sequence was generated, given the starting value of 6. Then answer Question 1 in your writeup.

You will write a program that allows the user to choose the value of N, and we will generate all the subsequent terms of the sequence.

It has not been mathematically proven that this sequence will always reach 1 and terminate. However, no one has yet found a value of N that fails to eventually reach 1.

xkcd's take:
xkcd on Collatz

Instructions

Create a new Python source code file named lab06a.py, substituting your name for the italicized text:

'''
Program: CS 115 Lab 6a
Author: Your name
Description: This program will ask the user for a value
   and tell the user whether the value is even or odd.
'''


def main():

    N = int(input('Enter a number: '))

    if N % 2 == 1:
        print(N, 'is odd.')
    else:
        print(N, 'is even.')


main()

Run your program using various input values, and be sure that it accurately reports whether the user's inputs are even or odd.

Modify your code as indicated by the blue pseudocode:

    if N % 2 == 1:
        # Compute the next term in the Collatz sequence for odd N, and set N to that value.
    else:
        # Compute the next term in the Collatz sequence for even N, and set N to that value.

    # Print the new value of N.

Note: you should use integer division (//) instead of floating-point division (/) so that the values appear as integers.

For example:

Enter a number: 8
The next term is 4.

or:

Enter a number: 3
The next term is 10.

To generate all the terms in the sequence, you will need a while loop. To practice while loop conditions, answer Question 2 in your writeup.
Put your if/else statements and your print statement inside a while loop:
```
while ...:
    if ...
    
    else ...

    print ...
```
The while loop condition should evaluate to True until you have finished the sequence, and then it should become False. Remember that the sequence ends when N reaches 1. The condition does not need to be long and involved -- it can be very short.

If you accidentally write an infinite loop, you can press Ctrl-C to force-quit your program.

Test your program using the following sample input/output sequences:

Enter a number: 8
The next term is 4.
The next term is 2.
The next term is 1.

Enter a number: 6
The next term is 3.
The next term is 10.
The next term is 5.
The next term is 16.
The next term is 8.
The next term is 4.
The next term is 2.
The next term is 1.

When your code is correct, call an instructor over to demo your program. This week, you will demo Parts A and C, but you will only submit your Part C code.
Continue to Part B.