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 154
- The diagonals of a regular nonagon divide it into 154 regions
- 154 is the smallest starting index of a string of exactly 3 consecutive equal digits in decimal expansion of Pi
- 154 = (1*5*4)*(1+5+4) - pi((1*5*4)*(1+5+4)), where pi(n) is the number of primes less or equal to n. Note that 154 is the smallest multidigit number with this property
Common Properties of 154
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 n-th lazy caterer number is the maximum number of pieces a (circular) pizza can be cut into with n (straight-line) cuts.
Unlike the situation with cake, everybody gets the toppings.
A number is said to be square-free if its prime decomposition contains no repeated factors.