Edit in JSFiddle

$(document).ready(function() {
   var table = $('#example').DataTable({
      'initComplete': function(){
         var api = this.api();

         // Initialize Typeahead plug-in
         $('.dataTables_filter input[type="search"]', api.table().container())
            .typeahead({
               source: function(query, process){
                  $.getJSON('https://api.myjson.com/bins/6hnjb', { q: query }, function (data){
                     return process(data);
                  });
               },
               afterSelect: function(value){
                  api.search(value).draw();
               }
            }
         );
      }
   });
});

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