If you want to be sure a specific person or company finds your Tweet, put an @ (the “at” symbol) in front of the Twitter name. Example: @LarryChaseWDFM.
Twitter calls these “mentions” and tracks who mentions you and what they say. When you mention others using the @ symbol, those people will see your Tweet, even if they don’t follow you.
Likewise, you’ll see any Tweet that mentions your Twitter handle, even if you don’t follow that particular Twitterer.
Most Twitter clients build this “mention” function in when you reply to a Tweet, but you can add the @ symbol manually as long as you use the correct Twitter handle. LC