Joker Classic 2022-04-01: Collatz In Sunbeams

I wrote some code to work in reverse, starting with a target number and going (ideally) down until 1 was reached. (In retrospect, I didn't get the reverse spelling completely correct; sorry! I imagine my version pronounced with a Spanish accent and sounding like "yoke toss.")

I realized that if the numbers got bigger and bigger, I'd have a halting problem-like problem to deal with. So, I just hoped that they'd end up hitting a loop (like 1 -> 4 -> 2 -> 1, if the problem didn't end with 1). I guess I'd know something was up when my computer spewed out of memory errors if it just kept going higher and higher. Anyway, my code:

def lloctaz(n, verbose=False):
    seen = {n}
    while n != 1:
        if verbose: print(n, end=' ')
        if n % 2 == 0:
            if verbose: print('/ 2 =')
            n = n // 2
        else:
            if verbose: print('* 3 + 1 =')
            n = n * 3 + 1
        if n in seen:
            print(n, '<-- !!! CYCLE DETECTED !!!')
            return False
        else:
            seen.add(n)
    if verbose: print(1)
    return len(seen)

def test(start):
    while lloctaz(start):
        start += 1
        if start % 1_000_000 == 0:
            print(start)

I let this run until I reached a cycle -- it took a *lot* longer than I expected.
>>> test(1)
1000000
2000000
3000000
[... big snip ...]
57677621523618000000
57677621523619000000
57677621523620000000
57677621523620152583 <-- !!! CYCLE DETECTED !!!
>>>

I investigated:
>>> lloctaz(57677621523620152583, True)
57677621523620152583 * 3 + 1 =
173032864570860457750 / 2 =
86516432285430228875 * 3 + 1 =
259549296856290686626 / 2 =
129774648428145343313 * 3 + 1 =
378914162223842065210 / 2 =
189457081111921032605 * 3 + 1 =
568371243335763097816 / 2 =
284185621667881548908 / 2 =
142092810833940774454 / 2 =
71046405416970387227 * 3 + 1 =
213139216250911161682 / 2 =
106569608125455580841 * 3 + 1 =
319708824376366742524 / 2 =
159854412188183371262 / 2 =
79927206094091685631 * 3 + 1 =
239781618282275056894 / 2 =
119890809141137528447 * 3 + 1 =
359672427423412585342 / 2 =
179836213711706292671 * 3 + 1 =
539508641135118878014 / 2 =
269754320567559439007 * 3 + 1 =
809262961702678317022 / 2 =
404631480851339158511 * 3 + 1 =
1213894442554017475534 / 2 =
606947221277008737767 * 3 + 1 =
1820841663831026213302 / 2 =
910420831915513106651 * 3 + 1 =
2731262495746539319954 / 2 =
1365631247873269659977 * 3 + 1 =
4096893743619808979932 / 2 =
2048446871809904489966 / 2 =
1024223435904952244983 * 3 + 1 =
3072670307714856734950 / 2 =
1536335153857428367475 * 3 + 1 =
4609005461572285102426 / 2 =
2304502730786142551213 * 3 + 1 =
6913508192358427653640 / 2 =
3456754096179213826820 / 2 =
1728377048089606913410 / 2 =
864188524044803456705 * 3 + 1 =
2592565572134410370116 / 2 =
1296282786067205185058 / 2 =
648141393033602592529 * 3 + 1 =
1944424179100807777588 / 2 =
972212089550403888794 / 2 =
486106044775201944397 * 3 + 1 =
1458318134325605833192 / 2 =
729159067162802916596 / 2 =
364579533581401458298 / 2 =
182289766790700729149 * 3 + 1 =
546869300372102187448 / 2 =
273434650186051093724 / 2 =
136717325093025546862 / 2 =
68358662546512773431 * 3 + 1 =
205075987639538320294 / 2 =
102537993819769160147 * 3 + 1 =
307613981459307480442 / 2 =
153806990729653740221 * 3 + 1 =
461420972188961220664 / 2 =
230710486094480610332 / 2 =
115355243047240305166 / 2 =
57677621523620152583 <-- !!! CYCLE DETECTED !!!
False
>>>

I couldn't find the sequence in OEIS; for that matter, I couldn't find *any* of the numbers in OEIS. I didn't get any hits for 57677621523620152583 on Google, either, but I imagine they'll come once people start solving this. Wolfram|Alpha gave its prime factorization as 79 × 103 × 541 × 571 × 22946140769, which doesn't seem to be super insightful.

I do like how the numbers went up and down like that -- there's something soothing, yet chaotic about that procedure.