222 (number) explained

222 (two hundred [and] twenty-two) is the natural number following 221 and preceding 223.

In mathematics

It is a decimal repdigit^[1] and a strobogrammatic number (meaning that it looks the same turned upside down on a calculator display).^[2] It is one of the numbers whose digit sum in decimal is the same as it is in binary.^[3]

222 is a noncototient, meaning that it cannot be written in the form n - φ(n) where φ is Euler's totient function counting the number of values that are smaller than n and relatively prime to it.^[4]

There are exactly 222 distinct ways of assigning a meet and join operation to a set of ten unlabelled elements in order to give them the structure of a lattice,^[5] and exactly 222 different six-edge polysticks.^[6]

Notes and References

1. A010785 . Repdigit numbers, or numbers with repeated digits.
2. A018846 . Strobogrammatic numbers: numbers that are the same upside down (using calculator-style numerals).
3. A037308 . Numbers n such that (sum of base 2 digits of n) = (sum of base 10 digits of n).
4. A005278 . Noncototients: n such that x-phi(x) = n has no solution.
5. A006966 . Number of lattices on n unlabeled nodes.
6. A019988 . Number of ways of embedding a connected graph with n edges in the square lattice.