Timeline for Computationally challenging integer sequences
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 26, 2023 at 2:50 | comment | added | Sidharth Ghoshal | I was exposed to this at a recreational math talk: oeis.org/A006983 | |
| Oct 25, 2023 at 12:39 | answer | added | G. Melfi | timeline score: 3 | |
| Aug 8, 2022 at 0:49 | answer | added | Gerry Myerson | timeline score: 2 | |
| Jul 21, 2022 at 2:18 | answer | added | Sam Hopkins | timeline score: 3 | |
| Jul 21, 2022 at 2:05 | answer | added | Per Alexandersson | timeline score: 5 | |
| Mar 6, 2017 at 20:57 | answer | added | Seva | timeline score: 6 | |
| Mar 6, 2017 at 5:59 | answer | added | none | timeline score: 9 | |
| Mar 6, 2017 at 5:03 | answer | added | Brendan McKay | timeline score: 10 | |
| Mar 3, 2017 at 6:35 | answer | added | Gerhard Paseman | timeline score: 13 | |
| Mar 3, 2017 at 0:55 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Added tag
|
| Mar 3, 2017 at 0:46 | comment | added | Anton | @Geoffrey Irving I do see a distinction, at least in comparison to Mersenne primes sequence A000043. We can actually hope that in a year or so GIMPS will find the answer whether $M_{37156667}$ is a 46th prime or not. Looking back to the link oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/difficulty, one criterion for marking an OEIS sequence with the "hard" keyword is if "A sequence ... is the target of a distributed search or computation". My question is about those sequences. | |
| Mar 2, 2017 at 19:03 | comment | added | Tom Copeland | In particular, I would be interested in an extension of the hard sequence oeis.org/A060638 per the discussion in mathoverflow.net/questions/260279/… and math.stackexchange.com/questions/2120390/…. | |
| Mar 2, 2017 at 15:09 | comment | added | Geoffrey Irving | @Anton: How is that different than the other hard sequences? I would claim that no hard line exists between better computational tools and theoretical advances. | |
| Mar 2, 2017 at 13:12 | comment | added | Anton | @GeoffreyIrving But can we really compute one of the unknown terms without introducing new theoretical ideas? Already in the case d=4, where the answer was known to be either 24 or 25, it was too time consuming to compute the result using standard methods, and Musin had to come up with a modification of Delsarte's method in order to provide a definitive answer. | |
| Mar 2, 2017 at 6:38 | comment | added | Geoffrey Irving | @Anton: Aren't kissing numbers just semialgebraic geometry, and thus computable in mere doubly exponential time? | |
| Mar 2, 2017 at 6:17 | comment | added | Anton | @NoamD.Elkies thanks, I think this comment can actually be regarded as a partial answer. The only thing that I want to mention is that not all of the sequences marked with "hard" keyword require computational tools to extend them. For example, the kissing number sequence A257479 is marked as "hard", but determination of unknown terms of this sequence requires deep theoretical investigations rather than computations. | |
| Mar 2, 2017 at 5:40 | comment | added | Noam D. Elkies | OEIS has a keyword "hard" for such sequences. See the "hard" paragraph in oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/difficulty (which notes Mersenne exponents as one example). | |
| Mar 2, 2017 at 5:15 | history | edited | Anton | CC BY-SA 3.0 |
Removed the sphere kissing problem as an example. It is more theoretical than computational.
|
| Mar 2, 2017 at 5:03 | comment | added | Anton | @ManfredWeis That's a very good point. I think the main criterion is that it should be potentially feasible to compute the next term if one has an efficient algorithm and sufficient computing power (e.g. access to a supercomputer). So the problem is computational rather than theoretical. Though being a good example, odd perfect numbers hardly qualify then. | |
| Mar 2, 2017 at 4:58 | comment | added | Manfred Weis | Is your question restricted to sequences that are known to exist? Otherwise the sequence of odd perfect numbers would qualify. From the Mersenne Primes example I conclude, that potentially finite sequences are also in scope of your question. | |
| Mar 2, 2017 at 4:45 | history | edited | Anton | CC BY-SA 3.0 |
deleted 14 characters in body
|
| Mar 2, 2017 at 4:37 | history | asked | Anton | CC BY-SA 3.0 |