In C++:

The Syracuse Sequence

The Syracuse Sequence is a sequence of numbers that can be generated with an algorithm that takes an input number n. It is named after Syracuse, NY, where it was originally studied. The function is part of a general class known as the '3n + 1' functions.

Here is the definition. The function starts with an input number, n, greater than or equal to 1.

If n is 1, the sequence stops.

If n is even, the next number is n / 2.

Else, n is odd and the next number is (3n + 1) / 2.

For example, if we start with n = 5, the sequence is:

5, 8, 4, 2, 1

Starting with n = 6, it will go a little longer:

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

One interesting aspect of this sequence: it appears that for any starting number, the sequence will always reach 1 (and stop), although this has not been proven. Some numbers (like 27) take many steps to reach 1.

Assignment

Write a recursive function syracuse() that accepts as input:

An integer for n

Another integer to specify the limit of the number of terms calculated. If the limit is reached, the sequence should stop.

Add any other parameters at your option. As with any recursive function, with a very deep sequence of function calls, the system will eventually run out of resources. The limit is useful to stop your program so that this does not happen.

Then, make your program output the following:

The input number 'n' and result of each call to syracuse(n)

Whether the sequence was aborted early because of the limit

The highest number reached

If the number of function calls to syracuse() reaches the limit, the program should stop printing any more numbers at that point.

Other requirements:

No global variables here! Use parameters to your syracuse() function.

Validate that the input number and limit are each greater than 1, looping with an error message and prompting until the input is valid (you can do this in main() before calling the function).

No need to loop for additional sequences. Your program can run once and exit.

Use a consistent C++ style in your program according to the guidelines.

Example Output (two separate runs)

Number: 5 Limit of terms: 10 Input Number syracuse(n) ------------------------------- 5 8 8 4 4 2 2 1 Highest number reached: 8 Number: 19 Limit of terms: 5 Input Number syracuse(n) ------------------------------- 19 29 29 44 44 22 22 11 11 17 Sequence was aborted early. Highest number reached: 44