Custom query to get post names beginning with a digit

The solution given by @RolandoMySQLDBA will give you all posts because you have a * and not a +. The * means to return zero or more matches, which is not what you want. In this case, you actually don’t need either, but just to match the first character. Try this:

$sql .= $wpdb->prepare( " AND $wpdb->posts.post_name REGEXP '^[0-9]'");