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 919
- 919 is the smallest multidigit palindromic number whose sum of digits shows up as a substring of the number
- 919 is the smallest number which is not the difference between two positive palindromes
- 919 is the smallest palindromic prime whose digital root equals its middle digits
- 919 is the smallest prime p such that p-1 and p+1 are both divisible by non-trivial cubes (919 - 1 = 2*33*17 and 919 + 1 = 23*5*23)
Common Properties of 919
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 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.
Undulating numbers are numbers of the form abababab... in base 10.
This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.