Timeline for Smallest set such that all arithmetic progression will always contain at least a number in a set
Current License: CC BY-SA 4.0
17 events
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| Jun 28, 2019 at 17:49 | history | edited | color | CC BY-SA 4.0 |
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| Jun 27, 2019 at 19:39 | comment | added | Timothy Chow | @RobertIsrael : The OP suggested taking the size of S to be the square of the length of the AP. In any case, the OEIS does contain tables (Pascal's triangle, Stirling numbers, etc.); it just lists things one row at a time. | |
| Jun 27, 2019 at 16:39 | comment | added | Robert Israel | @TimothyChow It may not be easy to find in OEIS since there are two parameters: the length of the AP and the size of $S$. | |
| Jun 27, 2019 at 16:23 | comment | added | color | @RobertIsrael I see. I will edit my question later. | |
| Jun 27, 2019 at 16:10 | comment | added | Robert Israel | Note that for $a = 15$, $d=3$, $a + 10 d \equiv 1 (\bmod 11)$, but it's not true that $a=d+1$. So your proof fails. | |
| Jun 27, 2019 at 16:05 | comment | added | Robert Israel | And your proposed solution does not intersect all the arithmetic progressions of length $10$. For example, it does not intersect $(15, 18, 21, 24, 27, 30, 33, 36, 39, 42)$. | |
| Jun 27, 2019 at 16:03 | answer | added | Robert Israel | timeline score: 11 | |
| Jun 27, 2019 at 15:59 | comment | added | Robert Israel | I think you mean there are $506$ arithmetic progressions of length $10$. This is $\sum_{d=1}^{11} (100 - 9 d)$. | |
| Jun 27, 2019 at 15:29 | comment | added | color | @TimothyChow Yes, but for small numbers like 2,3,4. How can I use the OEIS? | |
| Jun 27, 2019 at 14:44 | comment | added | Timothy Chow | For the last question (replacing 10 with $n$), have you computed the optimal number for $n\le 9$ and checked the OEIS? | |
| Jun 27, 2019 at 12:37 | comment | added | Robert Israel | This can be considered as a set-covering problem. Although set covering is NP-complete, I suspect this one is within the reach of current technology. | |
| Jun 27, 2019 at 10:42 | answer | added | Seva | timeline score: 12 | |
| Jun 27, 2019 at 8:21 | comment | added | Dima Pasechnik | good questions don't get forgotten. they pop up in searches, etc. | |
| Jun 27, 2019 at 7:02 | comment | added | color | @DimaPasechnik Thanks. I just afraid that my question will be forgotten and cannot be answered. | |
| Jun 27, 2019 at 6:24 | comment | added | Dima Pasechnik | it is not too unusual that questions here get answered, say, after a year, and not immediately. | |
| Jun 27, 2019 at 5:21 | history | edited | color | CC BY-SA 4.0 |
edited title
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| Jun 27, 2019 at 5:06 | history | asked | color | CC BY-SA 4.0 |