Timeline for Fastest growing set of odd numbers such that any even number can be expressed as the sum of two elements.
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Sep 5, 2011 at 20:51 | comment | added | Will Jagy | Right, this is a slowest growing where each new odd number is the largest that does get you a representation of the first missing even number, what Manjul Bhargava called the "truant." It seems, if you take instead the smallest that gives you the truant, you do get all odd numbers (you have all odd numbers up to $2k-1,$ the truant is $4k,$ the smallest new odd number that works is indeed $2k+1,$ as $2k-1 + 2k +1=4k$). So all that is at stake is the definition of "greedy" algorithm, which I interpret, in this setting, as taking the largest odd number that gets the truant. | |
| Sep 5, 2011 at 20:36 | comment | added | Greg Martin | well, the slowest growing set is the set of $all$ odd numbers.... | |
| Sep 5, 2011 at 20:29 | history | answered | Will Jagy | CC BY-SA 3.0 |