3.1.2.15 LAB: Collatz's hypothesis

LAB 

Estimated time

20 minutes

Level of difficulty

Medium

Objectives

Familiarize the student with:

• using the while loop;
• converting verbally defined loops into actual Python code.

Scenario

In 1937, a German mathematician named Lothar Collatz formulated an intriguing hypothesis (it still remains unproven) which can be described in the following way:

1. take any non-negative and non-zero integer number and name it c0;
2. if it's even, evaluate a new c0 as c0 ÷ 2;
3. otherwise, if it's odd, evaluate a new c0 as 3 × c0 + 1;
4. if c0 ≠ 1, skip to point 2.

The hypothesis says that regardless of the initial value of c0, it will always go to 1.

Of course, it's an extremely complex task to use a computer in order to prove the hypothesis for any natural number (it may even require artificial intelligence), but you can use Python to check some individual numbers. Maybe you'll even find the one which would disprove the hypothesis.

Write a program which reads one natural number and executes the above steps as long as c0 remains different from 1. We also want you to count the steps needed to achieve the goal. Your code should output all the intermediate values of c0, too.

Hint: the most important part of the problem is how to transform Collatz's idea into a while loop - this is the key to success.

Test your code using the data we've provided.

Test Data

Sample input: 15

Expected output:

46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 steps = 17

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Sample input: 16

Expected output:

8 4 2 1 steps = 4

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Sample input: 1023

Expected output:

3070 1535 4606 2303 6910 3455 10366 5183 15550 7775 23326 11663 34990 17495 52486 26243 78730 39365 118096 59048 29524 14762 7381 22144 11072 5536 2768 1384 692 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 steps = 62

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