Indigo, the purple made as a combination of red and blue does not exist on a rainbow in the classical sense.

The rainbow is the electromagnetic spectrum that our eyes can detect and our brain interprets these waves as colours. Essentially our brain can detect 3 colours separately, red, green and blue.

Light does not exist as a single colour in reality but instead is a lot of different colours hitting our eyes at almost the same time, which is why you can get a rainbow out of sunlight, but if you put a red light into a prism, you will only get red light out, or if you put other household lights into the same prism, the rainbow would be different, colours would be less intense or missing. That’s why light under different sources feel cool or warm but when you look at their spectrum as shown in the attached picture, they’re almost all one colour.

Your brain is able to interpret these colours extremely well with context and is the source of a lot of optical illusions.

So when you see a combination of red and blue together, your brain interprets it as indigo purple and is why it is different from a pure violet wavelength.

Also, as common as brown is in the world, it doesn’t exist on the rainbow, because it’s a dark orange colour and its weird to think about it that way.