Timeline for 0's in 815915283247897734345611269596115894272000000000
Current License: CC BY-SA 4.0
28 events
| when toggle format | what | by | license | comment | |
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| Jun 11, 2021 at 16:56 | comment | added | Pruthviraj | Maybe it will easy to solve in binary first. Where satisfied for 0!, 1!, 2!, 3! and 4!. | |
| Jun 1, 2021 at 8:10 | comment | added | A Stasinski | The point is that the question is not about the zeros in this number (which is a trivial question) but about the zeros in infinitely many other numbers. | |
| May 31, 2021 at 18:57 | comment | added | domotorp | I prefer to keep an air of mystery about 815915283247897734345611269596115894272000000000. | |
| May 31, 2021 at 17:13 | comment | added | YCor | I changed the title to "$0$'s in 40!=...", that is, added "40!". This makes the title less cryptic within the list of questions. I regret you reverted it. | |
| May 31, 2021 at 17:04 | history | rollback | domotorp |
Rollback to Revision 2
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| May 31, 2021 at 16:45 | comment | added | A Stasinski | The title would be improved (and less puzzling) if it were replaced by the sentence that is the actual question. | |
| May 31, 2021 at 16:19 | history | edited | YCor | CC BY-SA 4.0 |
made title less cryptic
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| S May 31, 2021 at 16:09 | history | suggested | none |
add open problem tag due to OEIS A137582 link @Spenser added in the comment thread
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| May 31, 2021 at 14:32 | review | Suggested edits | |||
| S May 31, 2021 at 16:09 | |||||
| May 29, 2021 at 19:19 | comment | added | none | @Malkoun I did a similar check before seeing your post, and ran it up to 40,000. OEIS A182049 mentioned by Jeppe Stig Nielsen implies it's been checked up to 100,000. I guess I could check somewhat further by letting a computer run through the weekend, but I doubt there's much point. | |
| May 29, 2021 at 16:32 | comment | added | Jeppe Stig Nielsen | $41!$ seems to be the last factorial number with no digit 9 in it. It looks like for $n\ge 42$, the decimal representation of $n!$ will contain all ten digits, even after trailing zeros have been removed. Edit: Found OEIS entry. | |
| May 29, 2021 at 9:24 | comment | added | Sylvain JULIEN | Ok, it seems you're Hungarian. Well, finding such words should not be too much of an issue :-) | |
| May 29, 2021 at 9:22 | comment | added | Sylvain JULIEN | As for the mnemonic, he can try to use 10 letters words, if they're not too uncommon in your native language. | |
| May 28, 2021 at 21:03 | comment | added | Malkoun | Interesting... I could not find another example for $41 \leq n \leq 16000$. I wrote a small Python program for that purpose, which checked the $n$s in the previous range one by one. | |
| May 28, 2021 at 20:48 | comment | added | domotorp | Then I suppose this answers my question as 'known open problem'. | |
| May 28, 2021 at 20:14 | comment | added | Spenser | One could call it the Zumkeller conjecture. | |
| May 28, 2021 at 19:44 | comment | added | Loïc Teyssier | @domotorp: oh, that's what I feared... :D | |
| May 28, 2021 at 19:16 | comment | added | Pietro Majer | I would learn a cyclic number instead, that he can use for magic tricks en.wikipedia.org/wiki/Cyclic_number | |
| May 28, 2021 at 19:07 | comment | added | domotorp | @Loïc Thanks, though a bit early, and it is not the 40th, but the 815915283247897734345611269596115894272000000000th ;) | |
| May 28, 2021 at 18:51 | comment | added | Jukka Kohonen | Oh, I understood it the wrong way! My bad. | |
| May 28, 2021 at 18:47 | comment | added | Will Brian | @JukkaKohonen: I mean that 40 probably is the largest number $n$ for which all the 0's in $n!$ appear at the end. | |
| May 28, 2021 at 18:39 | comment | added | Jukka Kohonen | @Will, did your back-of-envelope calculation provide any estimate on when it would happen? | |
| May 28, 2021 at 17:13 | comment | added | Will Brian | Using the heuristic that the digits of $n!$ are just random, followed by some zeroes at the end, you can calculate without too much trouble that the answer to your question is: probably yes. My (very crude) estimate puts it at a better than 99% chance. I don't know whether this heuristic is any good, and I doubt this way of thinking will lead to a real answer . . . but there you have it. | |
| May 28, 2021 at 17:09 | comment | added | Dave L Renfro | What follows doesn't answer your question, and probably won't contribute to an answer either, but a result by John Edward Maxfield -- A note on $N!$, Mathematics Magazine 43 #2 (March 1970), pp. 64-67 -- might be of interest: Given any positive integer $n,$ there exists a positive integer $N$ such that the decimal digits of $N!$ begin with all the decimal digits of $n,$ in their correct order. For more about this, see my answer to Short papers for undergraduate course on reading scholarly math. | |
| May 28, 2021 at 16:56 | comment | added | Loïc Teyssier | And by the way, happy 40th birthday ;) | |
| May 28, 2021 at 16:39 | comment | added | Dattier | Is there an integer n which does not divide 10 such that for any k integer with 10 does not divide a = n * k and a has a zero in its decimal places ? | |
| May 28, 2021 at 16:24 | comment | added | Per Alexandersson | Interesting question, but very difficult. I am not sure we even know if there are an infinite number of 0s in the decimal expansion of pi. (But it's believed this is the case) | |
| May 28, 2021 at 16:10 | history | asked | domotorp | CC BY-SA 4.0 |