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 18
- 18 is the smallest difference between an emirp and its reverse
- 18 is the only number that is twice the sum of its digits
- 18 is the only area of a rectangle with distinct integer sides such that the perimeter of the rectangle equals the area
- 18 is the only integer n such that n3 and n4 together contain each of the ten digits once
- The 18-Point problem asks to choose a sequence of points on an interval such that the first two are in different halves of the interval,the first three are in different thirds, and so on. The result is that it is impossible to find 18 such points
Common Properties of 18
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime 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.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.