Depends on what you want your final size and yield to be. Which is also very dependent on the strain also....but three weeks works, a month works, two months works, three...eight...
And Im not too sure what your are asking...are you asking what a good lighting time would be? There is only two lighting times...your Veg (18/6, varies somewhat) or your Flower (12/12, doesnt vary) Are you asking "if a three week old plant that has been vegging for three weeks is mature enought to switch to flowering or 12/12?"
I usually have mine at 18/6 for veg but 16/8 would work also with not too much effect on the growth...try bumpin it up to 18/6.