1) "I read on every other day." This is a very strange phrase, and Lewis Carroll made fun of it in "Through the Looking-Glass," but it means exactly what you said. "Every other day" means May 18th, 20th, 22nd, 24th, etc. Or May 19th, 21st, 23rd, 25th, etc. 2) "I read on alternate days, one on, one off." Or, "I alternate days when I read with days when I skip reading."