I'm not sure why you have more than one option with the same value, but this works
$(document).ready(function() {
$('input').change(function() {
var filter = $(this).val();
$('option').each(function() {
if ($(this).val() == filter) {
$(this).show();
} else {
$(this).hide();
}
$('select').val(filter);
})
})
})