Filter selectlist options based on user input while retaining items that were already selected

Html Code

<input type="text" class="radius" placeholder="SerialNo" data-bind="textInput: fromSerialNo" />
<br/>
<select data-bind="options: filteredInventoryList,
                   optionsText: function(item) {
                     return item.Id + ' (' + item.SerialNo + ')';
                   },
                   selectedOptions: selectedEquipment                   
                   " size="5" multiple="multiple" style="width: 300px;"></select>

Sample data (simplified):

  var inventory = [{
      Id: "1",
      SerialNo: "00001"
    },
    {
      Id: "2",
      SerialNo: "00002"
    },
    {
      Id: "3",
      SerialNo: "10003"
    },
    {
      Id: "4",
      SerialNo: "10004"
    }
  ];

Knockout Code:

function viewModel() {
  var _root = this;
  // User input serialNo for filtering
  _root.fromSerialNo = ko.observable();
  // selectedOptions of the select list
  _root.selectedEquipment = ko.observableArray();
  // parent list of all equipment
  _root.fromInventoryList = ko.observableArray(inventory);

  // filtered list based on serialNo user input (should including the previously selected items)
  _root.filteredInventoryList = ko.computed(function() {
      var filteredList = ko.observableArray(null);

      if (!_root.fromSerialNo()) {
        // This works perfect, allows the user to select one or more item from the list.
        return _root.fromInventoryList();
      }
      else {
        // The following works and allow users to filter the parent list of equipment

        // Only show items that begin with the SerialNo entered
        filteredList(ko.utils.arrayFilter(_root.fromInventoryList(), function (item) {
                    return item.SerialNo.startsWith(_root.fromSerialNo());
                }));

        return filteredList();
      }
  });
}

Everything works fine in terms of filtering the list based on the serial number the user inputs. Example here https://jsfiddle.net/JohnnyCodes/5h9pnqLg/.

Use Case:

• User selected the first item in (Id: 1, Serial 00001)
• User then enters 1 into the SerialNumber filter
  • I'd like the list to contain the selected item (Id: 1, Serial 00001) as well as the two items whose serial numbers begin with 1

Problem is, it's like there's some kind of recursive reference and the list starts to get wonky.

Enter 1 to filter then change it to 0 then change it back to 1

Here's an example, https://jsfiddle.net/JohnnyCodes/cs4z9xpg/5/

Pretty some this is something really simple and stupid I've overlooked but I've been going around in circles for a while now. Wouldn't mind another pair of eyes.

Thanks