@catfood,
Oh. My. I just found my mistake. I added an extra 1 onto one of the sequence numbers on accident. I believe we now have the same final answer, catfood - I got the 6839 start and 688 end.
I cannot believe I made such a stupid mistake after all those different patterns/calculations. And here I was about to submit my incorrect answer because I thought there was no way I could be wrong. LOL. Thank goodness I waited and compared with you!