Decks, Patios, Porches and Docks - removing green algae color

We have a deck that hasn't been treated in some time. Until we scrubbed & rinsed repeatedly with a bleach/water/detergent solution, it was slippery with green algae/mold.
Now that the fuzz & slippery areas are gone, the green color remains inside the boards.
The boards have lost their weathered, grey look & look brighter, but we can't get rid of the green & would like to stain with a semi-transparent stain which probably won't cover the green.
Home Depot suggested Behr's cleaner, which is only basically bleach anyway.
Does sodium percarbonate work any better on the green removal than bleach(sodium hyperchlorate) ? & which specific branded products do you suggest? (very few of them seem to say what the active chemicals are).
Thanks

I think it is sodium hypochlorite, but who's counting? Sometimes the ingredients aren't specifically listed because they don't want you to know you just paid $6.95 for a $1.00 bottle of bleach. Like Fuel Injector cleaner. It is listed as a petroleum distillate. Well, it is AVJet1 fuel, so, you just paid $4.50 for 10 cents worth of fuel.
Anyway, I would stick to the higher end cleaners, since they do put some other cleaners in with their main ingredients. Raw bleach does not do you deck much good, but the Behr and other cleaners would stand a better chance of cleaning. I hope you are using a pressure washer as well to help get in the grooves.