Twicker is the first (and only) Twitter client that focuses on search.
Its main purpose is to get search results based on your keywords and display them as clickable avatars. When you click on an avatar, Twicker expands to show you the tweet and offer you the option to reply.
Of course, you can use it as your primary Twitter client, since it also allows you to send non-reply tweets.
Please note that Twicker is currently unmaintained. However, I plan on getting it to version 2 this summer. You can still send feedback, I will try my best to help you.