JSFiddle - React, Tailwind, and code Playground

HTML

<ul id="1">
</ul>

<ul id="2">
</ul>

<ul id="3">
</ul>

JavaScript

var datearray =  {
    1367848800000: true,
    1367935200000: true,
    1368021600000: true,
    1368108000000: true,
    1368194400000: true,
    1368367200000: true,
    1368540000000: true,
    1368626400000: true,
    1368712800000: true
};

$(function() {
   
    var result = dateSequences(datearray);
    
    // Render
    $.each(result[0], function(i,d) {
        $("#1").append("<li>"+d+"</li>");
    })    
    $.each(result[1], function(i,d) {
        $("#2").append("<li>"+d+"</li>");
    });
    $.each(result[2], function(i,d) {
        $("#3").append("<li>"+d+"</li>");
    });
    
    console.log(result);
    
});

// Where magic happens
function dateSequences(array) {
  // parse json object to array of keys
    var keys = Object.keys(array);
    // sort it up
    keys = keys.sort();
    // convert them to dates
    var dates = new Array();
    $.each(keys, function(i) {
        dates.push(new Date(parseInt(keys[i])));
    });

    // now we have array of dates, search for sequential dates
    var final = new Array();
    var prevdate = undefined;
    var currentseq = 0;    
    $.each(dates, function(i, d) {
        // undefined?
        // first sequence
        if (prevdate == undefined) {
            final.push(new Array());
            final[currentseq].push(d);
        }
        else {
            // compare if difference to current date in loop is greater than a day
            var comp=new Date();
            comp.setDate(prevdate.getDate()+2);
            // Advance sequence if it is
            if (comp < d) {
                currentseq++;
                final[currentseq] = new Array();
            }
            // Push the date to current sequence
            final[currentseq].push(d);            
        }
        // store previous
        prevdate = d;
    });   
    
    return final;
}