# Threeven Numbers

We spend too much time enthralled by even numbers. We can instantly tell if a number is even or odd and often have preferences in the matter. In grade school we memorize rules like

- An
**even**plus an**even**is an**even** - An
**odd**plus an**odd**is an**even** - An
**even**plus an**odd**is and**odd**

And so forth to rules of multiplication. But this magical quality of
numbers really just means *evenly divisible by 2.* What is so special
about 2? Shouldn’t we just as well care if a number is divisible by 3?

So I am introducing **threeven numbers** as all numbers divisible by
3.

0, 3, 6, 9, 12, 15, …

are all threven numbers. But what about numbers that aren’t divisible
by 3? Numbers that are not divisible 2 are called *odd* so I guess
*throdd?*

There is, however, a slight problem. There seem to be more throdd numbers than threeven numbers.

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, …

To solve that we need to think about what an odd number is. If an even
number is some number *n times 2* or *2n* then odd numbers are *2n +
1*

This gives a nice way to think about threeven numbers as well. Every
threeven is *3n* and a throdd is *3n + 1* and we need to introduce
throdder numbers as *3n + 2*. There isn’t any reason that there should
only be two types of numbers. So instead of numbers that are divisible
by 2 and numbers that aren’t, we have numbers that are divisible by 3,
numbers that are 1 greater than a multiple of three and numbers that
are 2 greater than a multiple of three.

To recap

- Threeven =
*3n* - Throdd =
*3n + 1* - Throdder =
*3n + 2*

Now for handy rules of thumb.

- A
**threeven**plus a**threeven**is a**threeven** - A
**threeven**plus a**throdd**is a**throdd** - A
**threeven**plus a**throdder**is a**throdder** - A
**throdd**plus a**throdd**is a**throdder** - A
**throdd**plus a**throdder**is a**threeven** - A
**throdder**plus a**throdder**is a**throdd**

And, for multiplication

- A
**threeven**times a**threeven**is a**threeven** - A
**threeven**times a**throdd**is a**threeven** - A
**threeven**times a**throdder**is a**threeven** - A
**throdd**times a**throdd**is a**throdd** - A
**throdd**times a**throdder**is a**throdder** - A
**throdder**times a**throdder**is a**throdd**

Note: it appears that I am not the first to have discovered threeven numbers. And no you are stuck knowing about them as well.