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 55
- 55 is the largest number that is both triangular and Fibonacci. By the way, 55 has index ten in either sequence
- 55 is the smallest multi-digit triangular number which is a palindrome
- 55 is the product of the smallest sexy prime pair
- 55 is the only multi-digit Fibonacci number using one digit
- 55 is the smallest number sandwiched between two numbers that are products for four primes
- Not counting trivial 1, 55 is the smallest triangular number that is also square-pyramidal
Rare Properties of 55
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.
Common Properties of 55
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 odd if it is not divisible by 2.
Numbers that are not odd are even. 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.
A number is said to be square-free if its prime decomposition contains no repeated factors.
If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a triangle number.
Compare to square, pentagonal and tetrahedral numbers.