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 2003
- 2003 is the first prime year in our millennium
Rare Properties of 2003
The k-th hungry number is the smallest number n such that 2^n contains the first k digits of the decimal expansion of pi.
They are named hungry numbers because they try to eat as much "pi" as possible.
- ...,
- 74,
- 144,
- 144,
- 2003,
- 37929,
- 82810,
- 161449,
- ...
Common Properties of 2003
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.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.
A number is odd if it is not divisible by 2.
Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.
A prime is a positive integer greater than 1 that is divisible by no positive integers other than 1 and itself.
Prime numbers are opposite to composite numbers.
A number is said to be square-free if its prime decomposition contains no repeated factors.