Edit in JSFiddle

var searchtext = "";
var searchIndice = 0;

$(function() {
    $('#textsearch').keypress(function(event) {
        return doSearch(event, $(this));
    });
});

function doSearch(event, input)
{
    // annule
    $('#cadreTree a').css("background", "");
    $('#nbOccur').html("");
    
    var code = event.keyCode || event.which; 
    if (code == 13) 
    {               
        var valeurTxt = input.val();
                        
        if(searchtext == "") // 1er coup
        {
            searchtext = valeurTxt;
            searchIndice = 0;
        } else {
            if(searchtext == valeurTxt)
            {

            } else {
                searchIndice = 0; /// re-init
            }
        }
                
        if(valeurTxt.length > 3)
        {
            // récupere a en question
            var aHiglight = $('#cadreTree a:icontains("' + valeurTxt + '")');

            if(aHiglight != null)
            {                                
                aHiglight.css("background", "#F3EE33");     

                if(searchIndice >= aHiglight.length) // redemarre a 0 si l'indice demandé est supérieur aux resultats
                    searchIndice = 0;

                var leBon = aHiglight[searchIndice];

                searchIndice++;

                // position du scrool + position absolu de l'element surbrillance - le début du div englobant                                            
                $("#cadreTree").scrollTop($("#cadreTree").scrollTop() + $(leBon).position().top - $("#cadreTree").position().top);

                $('#nbOccur').html(searchIndice + " sur " + aHiglight.length);
            }
        }

        return false;
    }
    return true;
}

$.extend($.expr[":"], {
    "icontains": function(elem, i, match, array) {
        return (elem.textContent || elem.innerText || "").toLowerCase().indexOf((match[3] || "").toLowerCase()) >= 0;
    }
});

<div id="cadreTree">
    <ul>
        <li><a href="#">Test 1</a></li>
        <li><a href="#">information</a></li>
        <li><a href="#">le petit chat</a></li>
        <li><a href="#">Test 2</a></li>
    </ul>
</div>

<input type="text" id="textsearch" >
<label id="nbOccur" >&nbsp;</label>