# 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 1012

- 1012 is the smallest number n such that the period length of the 'Reverse and Subtract' trajectory of n is greater than 1
- 1012 is the smallest multiple of 11 in which the even positioned digits from left are odd and the odd positioned ones are even
- If considered in base 3, 1012 is the smallest number that doubles when reversed

## Common Properties of 1012

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.