There is no seven colored rainbow

Newton invented "indigo" as a rainbow color because he thought it would be more "esoteric" to be seven colors instead of the six there really are. Indigo is either a very dark purple or blue, not a color on it's own.

There is a real mystery color though, and it is brown, which is not represented by the rainbow.

There are four ways to make brown:

The mixture of all three primary colors, red yellow and blue

The mixtures of secondary colors

orange-green

orange-purple

green-purple

There you go, you learned something new today

Any color is merely an artificial label assigned to some range of wavelengths of light (or combination therein). Light does not divide itself into colors. So the rainbow has exactly as many colors as we want it to have.

Actual rainbow colors:

Very light red

Light red

Red

Dark red

Very Dark red

Orange

Purple

Light purple

Very light purple

You should credit your posts like this. Word for word from another site. Indigo is a color on the blue scale. It can describe the color move from blue to purple accurately. 

In many ways brown is the inverse of gray/grey, despite both seeming 'dull' to our eye.

At Justus Liebig University Giessen in Germany, psychologist Roland Fleming studies how we see objects around us.
“The only reason Newton came up with ‘indigo’ is because for occult reasons he believed there must be seven basic colours that come together to make white. It certainly has little to do with physics and a lot more to do with the relationship between perception and language,” Fleming said.

A rainbow is caused by sunlight and atmospheric conditions. Light enters a water droplet, slowing down and bending as it goes from air to denser water. The light reflects off the inside of the droplet, separating into its component wavelengths--or colors. When light exits the droplet, it makes a rainbow.

Yeah, wasn't talking to you. 

huh?