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 9376
- 9376 is the numerical equivalent of the word ZERO on a touch-tone telephone
- 9376 is the only four-digit automorphic number
Rare Properties of 9376
The number n is called an automorphic number if (the decimal expansion of) n2 ends with n. These numbers are also called curious.
It is curious, how for a k-digit automorphic number n there is another automorphic number -- 10k + 1 - n. For this to work with n=1, you have to treat 1 as a zero-digit number.
- ...,
- 76,
- 376,
- 625,
- 9376,
- 90625,
- 109376,
- 890625,
- ...
Common Properties of 9376
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
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 evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
The untouchable numbers are those that are not the sum of the proper divisors of any number.