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
10 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2019 at 23:30 | comment | added | James | Here's a python script to find the lexicographically least example, if there is one, using pruning to give a slight improvement over naive brute force (but still quite time intensive): github.com/jmsmdy/mathematical-calculations/tree/master/… | |
| Jul 2, 2019 at 5:19 | comment | added | Mikhail Tikhomirov | My brute-force confirms that there no 15. | |
| Jun 30, 2019 at 3:53 | comment | added | Robert Israel | I didn't find a $15$, but that doesn't prove there isn't one. | |
| Jun 28, 2019 at 20:43 | comment | added | EGME | So is 16 optimal? | |
| Jun 28, 2019 at 8:00 | comment | added | color | Thank you. Your answer is correct. How long did it take to find those numbers? Can you find the boundary of $|P|$? | |
| Jun 28, 2019 at 0:50 | history | edited | Robert Israel | CC BY-SA 4.0 |
added 115 characters in body
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| Jun 27, 2019 at 17:00 | comment | added | Robert Israel | I'm using a tabu search over sets of a given size to maximize the number of a.p.'s that intersect the set. Possible moves consist of replacing a member of the set with a nonmember. | |
| Jun 27, 2019 at 16:50 | comment | added | Robert Israel | I'm working on $|P|=16$. So far I've found a $P$ with $|P|=16$, namely $\{9, 18, 28, 29, 31, 40, 42, 51, 53, 56, 65, 69, 70, 77, 84, 91\}$, that intersects all but one of these arithmetic progressions, the exception being $({36, 43, 50, 57, 64, 71, 78, 85, 92, 99})$. | |
| Jun 27, 2019 at 16:12 | history | edited | Robert Israel | CC BY-SA 4.0 |
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| Jun 27, 2019 at 16:03 | history | answered | Robert Israel | CC BY-SA 4.0 |