I am trying to show that this is Turing Recognizable.The language A, that is a DTM, T, that halts on a minimum of one input.My justification is that of course it is because, you just need to check if an accept state is reachable. However, this seems like I am making it trivial.Is there something larger I am missing?EDIT: New IdeaLet M be a DTM that does this:For every string w in the language, simulate w on T. if it halts, accept. The only problem I see with this, is if a string causes it to loop forever, then it will never try the others. 
DTM that halts on a minimum one input
turing machines
Hint: Use the technique of dovetailing, mentioned in several of the comments. The idea is to maintain a growing list of simulated Turing machines, all of them copies $T_1,T_2,\ldots$ of the input Turing machine $T$, operating as follows:Initialize $T_1$ with the $1$st possible input, and run $T_1$ for one step.Initialize $T_2$ with the $2$nd possible input, and run $T_1$ and $T_2$ for one step each.Initialize $T_3$ with the $3$rd possible input, and run $T_1,T_2,T_3$ for one step each.And so on.You get the idea. It is perhaps not obvious how to maintain the states of several Turing machines at once, but you can figure it out on your own.