# 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 242

- 242 is the smallest number such that 2 to its power contains 000
- digits in Morse code can be represented in base 3 with 1 for a dot and 2 for a dash; Morse-coded zero in base 3 is evaluated to 242
- 242 is the smallest number n that starts a run of 5 numbers where all of which are products of 3 or more primes
- 242 is the smallest integer to start a run of four consecutive integers with the same number of divisors

## Common Properties of 242

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 *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.

A *palindrome* is a number that reads the same forward or backward.

*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.