Is it okay to tan 3 days after you get a tattoo?

Not at all. You want to wait about a good month after getting a tattoo before you go out in the sun to tan. Having a healing tattoo is a vulnerability out in the sun and it will do nothing but delay the healing time most likely. There is little chance of actual harm being done to your skin and body if you are not bathing in it for hours, but you should still avoid direct sunlight throughout the healing time. Also, once healed, excessive tanning will break down your tattoo and make the colors less vibrant over time as well.