In $1979,$ Douglas Hofstadter, Professor of Cognitive Science at the University of Indiana, wrote

G$$del$,$ Escher, Bach. The book won the Pulitzer Prize for Literature and has over the years

become one of the classics of computer science. Much of its charm comes from the

mathematical oddities and puzzles it contains, many of which can be expressed in the form of

computer programs. Of these, one of the most interesting concerns the sequence of numbers

formed by repeatedly executing the following rules some positive integer $n$ :

If $n$ is equal to $1,$ you've reached the end of the sequence and can stop.

If $n$ is even, divide it by two.

If $n$ is odd, multiply it by three and add one.

Although is also goes by several other names, this sequence is often called the hailstone

sequence because the values tend to go up and down before coming back to $1,$ much as

hailstones in the clouds in which they form.

Write a C$++$ program that reads in a number from the user and then generates the hailstone sequence

from that point, as in the following sample run:

Enter a number: $15$

$15$ is odd, so I multiply by $3$ and add $1$ to get $46$

$46$ is even, so I divide it by $2$ to get $23$

$23$ is odd, so I multiply by $3$ and add $1$ to get $70$

$70$ is even, so I divide it by $2$ to get $35$

$35$ is odd, so I multiply by $3$ and add $1$ to get $106$

$106$ is even, so I divide it by $2$ to get $53$

$53$ is odd, so I multiply by $3$ and add $1$ to get $160$

$160$ is even, so I divide it by $2$ to get $80$

$80$ is even, so I divide it by $2$ to get $40$

$40$ is even, so I divide it by $2$ to get $20$

$20$ is even, so I divide it by $2$ to get $10$

$10$ is even, so I divide it by $2$ to get $5$

$5$ is odd, so I multiply by $3$ and add $1$ to get $16$

$16$ is even, so I divide it by $2$ to get $8$

$8$ is even, so I divide it by $2$ to get $4$

$4$ is even, so I divide it by $2$ to get $2$

$2$ is even, so I divide it by $2$ to get $1$

One of the fascinating things about the hailstone sequence is that no one has yet been able to

prove that the process always stops. The number of steps in the process can get very large, but

somehow, it always seems to climb back down to one.