Write a script that asks for an integer (n) and then computes the following based on the value of the integer...

2) Write a script that asks for an integer (n) and then computes the following based on the value of the integer:

While the value of n is greater than 1, replace the integer with half of its value (n/2) if the integer is even. Otherwise, replace the integer with three times its value, plus 1 (3*n + 1).

Make a provision to count the number of values in (or the length of) the sequence that results.

Example calculation: If n = 10, the sequence of integers is 5, 16, 8, 4, 2, 1 and so the length is 6.

Make a plot of the length of the sequence that occurs as a function of the integers from 2 to 30. For example, when n = 10, the length is 6 while for n = 15, the length is 17.

Is there any pattern? Try larger numbers to see if any pattern occurs. Is there any integer for which the sequence does not terminate?