1.  A function that produces the Collatz sequence and counts the number of terms.

2.  A main function that calculates interesting values about the Collatz sequence.

1.The Collatz Sequence

1. The rules for the Collatz Sequence are pretty straight forward:

3.  Start with an integer n > 1.

4.  Given a current term n, if n is even, the next term is n=2, if it is odd, the next term is 3n + 1.

5. Repeat until the last term is 1.

For examples: starting with n = 3, we get the sequence 3, 10, 5, 16, 8, 4, 2, 1.

2. It is an open question as to whether or not the sequence always returns to one for every starting value.

2. To Do and Turn In

1. The end result will be a .m file containing the main function, the Collatz function, and possibly other supporting functions.

2. The Collatz function should have one input and one output, the input is the starting number n, and the output is the number of terms in the sequence (the Collatz length), including the last term of 1. So in the example above for n = 3, the Collatz length is 8.

3. As usual, the main function will be in charge. It should be in charge of getting all the results calculated and in printing the results.

4. There are 3 results you need to produce:

(a) The Collatz length for n = 2; 3; . . .; 20 in a nice table (of course!).

(b) The first integer n for which the Collatz length is greater than 500. Display the integer and it's Collatz length.

(c) The integer n between 1 and 100 (inclusive) with the largest value for the ratio of it's Collatz length to itself. Display the integer, it's Collatz length and the ratio.

5. You'll need to figure out what kind of loop you need to use in each case.

6. As before you can have the main function do all the work (except for what the Collatz function does), or you can have subfunctions that do all or part of the work. The main function should, in any case, be totally responsible for displaying all the results.

7. When you are done, comment it well and publish the results as a PDF. Submit the PDF.