Collatz Variant

Math 242 practice problems

Name: _________________

Learning Goals: Use computation to discover properties of iterated functions.

Your task: Complete the two exercises below.

Due: Friday, March 15, at 5:00pm. Upload your solution as a Mathematica notebook to the Collatz Variant assignment (Moodle link).

Grading: If you use computation to find the correct answer to each question below, you will receive a Satisfactory grade for each problem.

Need help? Review the notes from class (which are posed on the course web site), talk with your classmates, email Prof. Wright, or visit the help session.

Problem 1

In class, we observed three distinct cycles that occur when iterating the ColVar function on positive integers. Consider the ColVar trajectories starting with integers n∈{1,2,3,...,1000}. How many times does each of the three cycles occur in these 1000 trajectories?

Hint: How many of these trajectories contain a 1? How many contain the number 5? How many contain 17?

Problem 2

Define the height of a ColVar trajectory to be the greatest integer that occurs in the trajectory. What is the most common height in the first 1000 ColVar trajectories?