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 42
- The number 42 is The Ultimate Answer to The Ultimate Question of Life, the Universe and Everything
- 42 is the number of spots on a pair of dice (submitted by Ken Knowlton)
- 42 is the alphanumeric value of FIVE
- The magic constant of a magic 3-by-3-by-3 cube is 42
- Number 42 on the web:
- 42 is the smallest abundant odious number
- 42 is the smallest sphenic Catalan number, where sphenic means a product of three distinct primes
Rare Properties of 42
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 n-th Catalan number is equal to (2n choose n)/(n+1) = (2n)!/(n!(n+1)!).
There are many ways Catalan numbers can be interpreted; there are some cool pictures here and the Wikipedia article is very good.
The number is called pronic if it is the product of two consecutive numbers.
They are twice triangular numbers.
Common Properties of 42
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 odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
A number is said to be square-free if its prime decomposition contains no repeated factors.