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.