Apache wrote:

> I'm not an expert in this, but if green is already brighter shouldn't that
> be compensated by a lower factor (like .114) instead of making it even more
> bright in comparison to the other two colors?

Not for getting the gray level.
When using gray, the order of colour is :

Black,  Blue,    Red,   Magenta, Green, Cyan,   Yellow and White.
<0,0,0>,<0,0,1>,<1,0,0>,<1,0,1>,<0,1,0>,<0,1,1>,<1,1,0> and <1,1,1>

Yellow is very light gray.
Green is middle grey
Red is dark grey
and Blue is very dark grey.

Try using the formula and then sort the values. Check the order!

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