"Special" Numbers

Didn't feel like writing a story so... We all know that 2 is the smallest prime number, 6 is a perfect number, and i is the number SQRT(-1) but do you know about narcissistic numbers? Or how about a Keith Number? Well, below I list the weirdest descriptor of numbers you probably don't know, or need to know (though it would be cool on a MAO test...).

1. Narcissistic Numbers - The official definition of a narcissistic number is this:

An -digit number that is the sum of the th powers of its digits is called an -narcissistic number.

Basically what its saying is that you take a random number's digit(s) and then raise each digit to the number of numbers in the random number. Finally add it all up. If it equals to itself, then it's a narcissistic number.

2. Keith Number - The definition is this:

A Keith number is an -digit integer 9" border="0" height="14" width="34"> such that if a Fibonacci-like sequence (in which each term in the sequence is the sum of the previous terms) is formed with the first terms taken as the decimal digits of the number , then itself occurs as a term in the sequence.

To explain this, it's best to look at an example. 197 is a Keith Number due to the fact that 1, 9, 7, , , , , . It's basically a Fibonacci sequence on a different starting point.

3. Kaprekar Number - Definition:

Consider an -digit number . Square it and add the right digits to the left or digits. If the resultant sum is , then is called a Kaprekar number.

Consider this, 81 is a Kaprekar number because 8 + 1 = 9 and 9 squared is 81.

-runiteking1

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