# 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 383

- 383 = prime(3*8*3) + σ(3+8+3) — Note that 383 is the smallest number with this property
- 383 is the smallest prime which can be represented as sum of a prime and its reverse (241 + 142 = 383)
- 383 is the sum of the first 3, three-digit palindromic primes: 101, 131 and 151
- 383 is the first multidigit palindromic prime to appear in the decimal expansion of pi
- 383 is the smallest palindromes expressible as the sum of 3 consecutive palindromic primes
- 383 = prime(3*8*3) + φ(3*8*3). Note that 383 is the smallest prime with this property

## Common Properties of 383

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 *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.