Timeline for Floor function of powers of $2$
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Apr 18, 2017 at 14:30 | comment | added | Mariusz Iwaniuk | @PaulAljabar.I'm engineer and math hobbyst,but proving the convergence,well: You have to ask this question to math.stackexchange.com maybe someone smarter will answer. | |
| Apr 18, 2017 at 14:04 | comment | added | Paul Aljabar | Thanks Mariusz, very interesting. How does one go about proving the convergence of the series expansion of $\log(1-z)$ for $|z| = 1$, which seems to be relied on in the expression? | |
| Apr 18, 2017 at 14:02 | comment | added | Paul Aljabar | I've found out, since writing the above, that algebraic numbers are indeed computable. As $\sqrt{2}$ is algebraic, it must be computable (at least algorithmically). | |
| Apr 17, 2017 at 8:19 | comment | added | user3141592 | On the other hand, if you try to work with that fornula involving logs you will eventually get stuck at an expression of the form $\arctan (\tan(f(n))$ or something similar, which returns you to the original floor function | |
| Apr 17, 2017 at 7:46 | comment | added | user3141592 | That seems interesting. Maybe, we now have the recipe and the ingredients. The problem would be joining both things | |
| Apr 17, 2017 at 6:02 | comment | added | Mariusz Iwaniuk | @PaulAljabar.Maybe this helps:community.wolfram.com/web/community/groups/-/m/t/1063480 | |
| Apr 16, 2017 at 21:01 | answer | added | Mariusz Iwaniuk | timeline score: 2 | |
| Apr 16, 2017 at 19:55 | history | edited | user3141592 | CC BY-SA 3.0 |
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| Apr 16, 2017 at 19:40 | comment | added | Paul Aljabar | If it were possible to obtain a closed form expression for all $n$, then, by restricting to odd values $n$, we could obtain a closed form expression for the values of OEIS A084188 - This would mean that we could derive a closed expression for the $n^{th}$ digit in the binary representation of $\sqrt{2}$, which I don't think is possible given that it is irrational. | |
| Apr 16, 2017 at 19:35 | comment | added | user3141592 | The main idea behind my "Edit" was trying to establish a recursive formula | |
| Apr 16, 2017 at 19:28 | history | edited | user3141592 | CC BY-SA 3.0 |
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| Apr 16, 2017 at 4:42 | comment | added | Claude Leibovici | This is sequence $A065732$ in $OEIS$. Nothing more than what Grant B. Commented. | |
| Apr 16, 2017 at 0:18 | comment | added | Grant B. | This is just the greatest perfect square less than or equal to $2^n$. For instance, $3\to4$, $5\to25$, $6\to64$. There's not really a closed form for it other than what you have written. | |
| S Apr 15, 2017 at 22:10 | history | suggested | DMcMor | CC BY-SA 3.0 |
Fixed delimiter sizes
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| Apr 15, 2017 at 22:01 | review | Suggested edits | |||
| S Apr 15, 2017 at 22:10 | |||||
| Apr 15, 2017 at 21:50 | history | asked | user3141592 | CC BY-SA 3.0 |