F12 > Console (Firefox: Ctrl+Shift+K, Chrome: Ctrl+Shift+J)

fake_random-org.js

(function() {

    var setResult = [11, 22, 33, 44, 55, 69],


        total = setResult.length,
        count = 0,
        iframe = document.getElementById('homepage-generator').getElementsByTagName('IFRAME')[0],
        iframeDocument = iframe.contentDocument || iframe.contentWindow.document,
        generator = iframeDocument.getElementById('true-random-integer-generator-button'),
        result = iframeDocument.getElementById('true-random-integer-generator-result'),
        min,
        max,
        loadEffect,
        
        randomNumber = function(x, y) {
            return Math.floor((Math.random() * (y + 1 - x)) + x);
        };


    generator.removeAttribute('onclick');
    generator.onclick = function() {

        min = parseInt(iframeDocument.getElementById('true-random-integer-generator-min').value, 10);
        max = parseInt(iframeDocument.getElementById('true-random-integer-generator-max').value, 10);
        if (min >= max) {
            max = ++min;
            iframeDocument.getElementById('true-random-integer-generator-max').value = max;
            result.innerHTML = randomNumber(min, max);
            return;
        }

        result.innerHTML = '<img src="/util/cp/images/ajax-loader.gif" alt="Loading..." />';

        clearTimeout(loadEffect);
        loadEffect = setTimeout(function() {
            result.innerHTML = (count < total) ? setResult[count] : randomNumber(min, max);
            count++;
        }, ((Math.floor(Math.random() * 5) + 3) * 100));

    };

})();

Bookmarklet version

https://jsfiddle.net/baivong/rhecyrm4/show/

(function() {

    if (location.href !== 'https://www.random.org/') {
        var checkHost = confirm("Bookmarklet doesn't work on this page.\nDo you want to open Random.Org?");
        if (checkHost) location.href = "https://www.random.org/";
        return;
    }

    var setResult = prompt('Please enter a series of numbers, separated by semicolons:', '11;22;33;44;55;69');
    if (setResult === null || setResult.trim() === '') return;
    setResult = setResult.split(';');


    var total = setResult.length,
        count = 0,
        iframe = document.getElementById('homepage-generator').getElementsByTagName('IFRAME')[0],
        iframeDocument = iframe.contentDocument || iframe.contentWindow.document,
        generator = iframeDocument.getElementById('true-random-integer-generator-button'),
        result = iframeDocument.getElementById('true-random-integer-generator-result'),
        min,
        max,
        loadEffect,

        randomNumber = function(x, y) {
            return Math.floor((Math.random() * (y + 1 - x)) + x);
        };


    generator.removeAttribute('onclick');
    generator.onclick = function() {

        min = parseInt(iframeDocument.getElementById('true-random-integer-generator-min').value, 10);
        max = parseInt(iframeDocument.getElementById('true-random-integer-generator-max').value, 10);
        if (min >= max) {
            max = ++min;
            iframeDocument.getElementById('true-random-integer-generator-max').value = max;
            result.innerHTML = randomNumber(min, max);
            return;
        }

        result.innerHTML = '<img src="/util/cp/images/ajax-loader.gif" alt="Loading..." />';

        clearTimeout(loadEffect);
        loadEffect = setTimeout(function() {
            result.innerHTML = (count < total) ? setResult[count] : randomNumber(min, max);
            count++;
        }, ((Math.floor(Math.random() * 5) + 3) * 100));

    };

})();