Timeline for Is there an infinite increasing sequence of naturals for which Landau's function can be efficiently computed?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 9, 2015 at 12:46 | comment | added | joro | @GerryMyerson I believe your disproved conjecture contradicts the asymptotic of $g(n)$. | |
| Jan 6, 2015 at 15:56 | history | edited | joro | CC BY-SA 3.0 |
added 146 characters in body
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| Jan 6, 2015 at 15:47 | comment | added | joro | @AlexanderBors very good point, thanks! Will try to edit to make it saner... | |
| Jan 6, 2015 at 15:32 | comment | added | Gerry Myerson | Yes, there's a smaller example at $n=100=2+3+\cdots+23$, where $g(n)=(16)(9)(5)(7)(11)(13)(17)(19)$. | |
| Jan 6, 2015 at 15:23 | comment | added | joro | @GerryMyerson you can verify this in the OEIS b-file: oeis.org/A000793/b000793.txt | |
| Jan 6, 2015 at 15:20 | comment | added | joro |
@GerryMyerson yours would have been very nice, but I think it can be something else: for $n=\sum_{p \le 43}=281$ g(n) factors as 2^4 * 3^2 * 5^2 * 7 * 11 * 13 * 17 * 19 * 23 * 29 * 31 * 37 * 43
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| Jan 6, 2015 at 14:59 | comment | added | Gerry Myerson | If $n$ is the sum of the first $k$ primes, can $g(n)$ be anything other than the product of those primes? | |
| Jan 6, 2015 at 14:53 | comment | added | Alexander Bors | Since $\mathrm{log}\hspace{2pt}g(n)\sim\sqrt{n\cdot\mathrm{log}\hspace{2pt}n}$, the number of ciphers of $g(n)$ alone is already too large to allow for computation in time polynomial in $\mathrm{log}\hspace{2pt}n$ on any infinite set of values for $n$. | |
| Jan 6, 2015 at 12:06 | history | asked | joro | CC BY-SA 3.0 |