In LR I choose to edit an image in photoshop. It opens up in photoshops fine. I don't edit anything, just choose to export it. The initial and exported image colors differ dramatically. The blue turns to purple. Please advise.
The shift in color is caused by viewing an image with the ProPhotoRGB colorspace using a viewer that assumes the image has the sRGB colorspace.
The image should have a ProPhotoRGB colorspace and be 16-bits when you're working in PS from LR; however, you should use Edit / Convert to Profile / sRGB before saving the final version of the image to be viewed in a browser from the internet. You also need to save the sRGB color profile with the image out of PS.
In other words ProPhotoRGB and 16-bits are good workspace parameters but the final version needs to be sRGB for viewing outside of LR and PS.