**9**

*Great Number Sequences: Prime, Fibonacci, and Hailstone*

**What Are Number Sequences?**

The answer to this question is that number sequences are simply lists of numbers appearing in a particular order. For example, the sequence 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is the list of the natural numbers or integers. The sequence 1, 3, 5, 7, 9, 11 is the list of the odd integers and the sequence 1, 4, 9, 16, 25, 36 is the list of the squares of the integers.

Another example: The sequence 1, 2, 4, 8, 16, 32, 64 is the list of numbers generated by doubling successive numbers. Sometimes, as in this case, a mathematical formula can produce the sequence of numbers. In this example, the formula is *N = 2*^{n}, where *N* is the magnitude of the *nth* number of the sequence. ...