JS

function test(p) {
    var u = 'elsa';
    var used = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
    var ok = false;
    if (u === 'elsa') {
        if (p > 0 && p.length == 10) {
            ok = true;
            for (i = 1; i <= 10; i++) {
                var digit = p.charAt(i - 1);
                var part = p.substring(0, i);
                if (used[digit] != 0 || part % i != 0) {
                    ok = false
                }
                if (used[digit] == 0) {
                    used[digit] = 1
                }
            }
        }
    }
    return ok;
}

function pad(num, size) {
    var s = "000000000" + num;
    return s.substr(s.length - size);
}
var permutations = require('steinhaus-johnson-trotter');
var generate = permutations("123");
for (p = 0; p <=9999999999; p++) {
    num = generate();
    var ok = test(pad(num, 10));
    if (ok) {
        console.log(num);
        break;
    }
}