I have a VF form with one input field and an 'Enter' command button. Since the input value is almost always the same length, I want to automatically submit the form when the input field is filled.  I'm using jQuery to determine when the field is filled but I cannot figure out how to submit the form. Eventually I want to convert this page to use AJAX so just the form and message are rerender then create a mobile version of the UI. Any suggestions are greatly appreciated.

Here's the code:

<apex:page docType="html-5.0" controller="MyController" standardStylesheets="true" showHeader="true" sidebar="false">
<apex:includeScript value="{!URLFOR($Resource.Mobile_Design_Templates, 'Mobile-Design-Templates-master/common/js/jQuery2.0.2.min.js')}"/>
<script>
    j$ = jQuery.noConflict();
    j$(document).ready( function() {
        j$("input[id$='lu']").keyup( function() {
            if (j$(this).val().length == 20) {
                alert( "Len = 20" );  // this fires
                j$("form[id$='form']").submit();  // form not submitted, input field retains entered value
            }
        });
    });
</script>

<apex:form id="form">
    <apex:pageBlock >
        <apex:pageBlockSection >
            <apex:outputLabel value="LU"/ >
            <apex:input id="lu" type="text" value="{!inputLU}" html-maxlength="20" />
        </apex:pageBlockSection>
        <apex:pageBlockSection >
            <apex:commandButton action="{!updateLU}" value="Enter"/>
        </apex:pageBlockSection>  
    </apex:pageBlock>
    <apex:pageMessages />
</apex:form>
</apex:page>