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 8
- 8 is the only composite cube in the Fibonacci sequence
- 8 is the dimension of the octonions and is the highest possible dimension of a normed division algebra
- 8 is the smallest number (except 1) which is equal to the sum of the digits of its cube
- "Eight" is the lexicographically first string representing an integer in English
- 8 is the sum of two first two odd primes
- 8 is the largest Fibonacci number with a prime neighbor
- the smallest number of acute triangle a square can be triangulated into is 8
- The smallest number of perfect riffle out-shuffles to return a standard deck of cards to its original order is 8
Rare Properties of 8
The n-th cake number is the maximum number of pieces a (cylindrical) cake can be cut into with n (straight-plane) cuts.
Unfortunately, not everybody gets the frosting. If you cut pizza rather than cake, you get lazy caterer's numbers.
The number n is a cube if it is the cube of an integer.
Fibonacci numbers are numbers that form the Fibonacci sequence. The Fibonacci sequence is defined as starting with 1, 1 and then each next term is the sum of the two preceding ones.
Fibonacci numbers are very common in nature. For example, a pineapple has 8 spirals if you count one way, and 13 if you count the other way.
A k-digit number n is called narcissistic if it is equal to the sum of k-th powers of its digits. They are also called Plus Perfect numbers.
A number is a power of 2 if it is 2 to some power.
Common Properties of 8
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.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.
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.