Timeline for Does this sequence ever end?
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 15 at 20:37 | vote | accept | look at me | ||
| May 15 at 14:55 | comment | added | Sam Hopkins | Does this answer your question? Implications of the disproof of the "climb-to-a-prime" conjecture | |
| May 15 at 14:28 | comment | added | Timothy Chow | I think of the situation as akin to a multi-armed bandit problem. Do I explore by pulling on the Collatz-palindrome-aliquot-etc arm, or do I exploit by pulling on the current-hot-topic arm? My expectation is that the optimal strategy involves occasional exploration. Gauss refused to pull on the Fermat's-last-theorem arm, which is fine, but luckily for us some other people did pull on that arm. | |
| May 15 at 13:26 | comment | added | Timothy Chow | @StanleyYaoXiao I agree that less talented mathematicians must take fewer risks when it comes to their career, but my point is that it is not true that research mathematicians, even those of the caliber of Conway, necessarily consider such questions to be "not serious." Maybe the problem goes nowhere, but maybe it doesn't. One can't be sure of such things ahead of time. Any individual mathematician may choose, for whatever combination of reasons, not to work on a particular problem, but that doesn't necessarily mean there's anything wrong with the problem itself. | |
| May 15 at 13:04 | comment | added | Stanley Yao Xiao | @TimothyChow sure, but not all of us (in fact, few if any) are John Conway | |
| May 15 at 12:45 | comment | added | Timothy Chow | @StanleyYaoXiao We can all be grateful that John Conway chose to ignore the conventional wisdom about what professional mathematicians are "supposed to" work on, and instead carved out his own path. | |
| May 15 at 12:09 | answer | added | Timothy Chow | timeline score: 23 | |
| May 15 at 2:01 | history | edited | look at me | CC BY-SA 4.0 |
added 118 characters in body
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| May 15 at 1:57 | comment | added | look at me | $13532385396179 = 13·53^2·3853·96179$, This apparently is the smallest number that $f(n)=n$ | |
| May 15 at 1:53 | comment | added | Gerry Myerson | $2^59^2=2592$, as noted by Dudeney. Alas, $9$ isn't a prime. | |
| May 14 at 19:01 | comment | added | Sidharth Ghoshal | Picking one such question and obsessing over it might be very dangerous for reasons identical to the Collatz Conjecture being described as a mathematical disease. I don't know for sure but I'm sure there are a lot of "easy to state" questions that are going to require techniques beyond ANYTHING that has been invented or will be invented for centuries to come in order to crack. And that's the reality of it. | |
| May 14 at 19:00 | comment | added | Sidharth Ghoshal | I think moverflow should be open to it too! I will defend slightly @AlecRhea 's point in that its very easy to make hard questions by mixing string manipulation with elementary number theory. Despite that I think it's good to allow these in the sense that I don't think this will get answered today. But 200 years from now we might ask "what are all the questions on early mathoverflow using basic arithmetic and string manipulation that we haven't resolved yet" and this can end up on a list sorted by "complexity" and eventually hacking at it can prove to be useful. | |
| May 14 at 18:25 | history | became hot network question | |||
| May 14 at 18:20 | comment | added | mathoverflowUser | @StanleyYaoXiao: It is a question out of curiosity. Mathematics should be open for such questions. | |
| May 14 at 18:07 | answer | added | mathoverflowUser | timeline score: 8 | |
| May 14 at 16:51 | comment | added | Stanley Yao Xiao | @AlecRhea sure, I didn't vote to close, just to say that problems of this sort are easy to generate and usually go nowhere. Number theorists in particular have to be vigilant about catching "mathematical diseases" (Tim Gowers used this phrase to describe the Collatz conjecture, which is actually somewhat reminiscent of this question), i.e., getting stuck thinking about a simple-sounding problem that ultimately goes nowhere. | |
| May 14 at 16:26 | comment | added | Alec Rhea | @StanleyYaoXiao But should we be closing questions just because 'most research mathematicians in that field wouldn't be interested in this problem'? What people are interested in (even active researchers in a given field) doesn't dictate what is and isn't mathematics, nor does it determine what is/isn't research level imo. For a really extreme example, most of Cantor's contemporaries were uninterested in his work. | |
| May 14 at 16:12 | comment | added | Stanley Yao Xiao | @AlecRhea there lacks a reason to close that sounds more like "this is probably hard, but not a problem that would be considered a serious question by researchers". In number theory there are many such examples: take your favourite arithmetic sequence and take your favourite polynomial and you can ask: does this polynomial take on infinitely many values from that arithmetic sequence? One cannot consider ALL such questions interesting. | |
| May 14 at 15:29 | comment | added | Alec Rhea | 3 votes to close as not research level? Is this question trivial for experts with the relevant knowledge base? It doesn't look trivial to me, but I have no expertise in this area. | |
| May 14 at 6:52 | comment | added | HenrikRüping | Just to make sure that the sequence is precisely defined: You take the prime decomposition, order the occuring primes increasingly from left to right, omit the exponent 1 whenever it occurs, and of course 1 itself is not a prime number. Furthermore you work in base 10 (which also could affect the result). | |
| May 14 at 5:25 | review | Close votes | |||
| May 23 at 3:11 | |||||
| S May 14 at 4:57 | review | First questions | |||
| May 14 at 6:04 | |||||
| S May 14 at 4:57 | history | asked | look at me | CC BY-SA 4.0 |