# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 5050

- 5050 is the sum of the first 100 integers

## Common Properties of 5050

The number n is called an *apocalyptic power* if 2^{n} contains the consecutive digits 666 (in decimal).

A positive integer greater than 1 that is not prime is called *composite*.

Composite numbers are opposite to prime numbers.

The number n is *deficient* if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant numbers.

A number is *even* if it is divisible by 2.

Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.

The number n is *evil* if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a *triangle* number.

Compare to square, pentagonal and tetrahedral numbers.

*Undulating* numbers are numbers of the form abababab... in base 10.

This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.