Addition-chain exponentiation - Revision history

en>Andyhowlett at 00:41, 15 December 2014

2014-12-15T00:41:30Z

en>Qwertyus: Gordon ref: {{cite journal}}, url that is outside the paywall

2013-11-11T14:57:34Z

Gordon ref: {{cite journal}}, url that is outside the paywall

← Older revision		Revision as of 16:57, 11 November 2013
Line 1:		Line 1:
	~~Let~~'~~s look an actual registry scan plus certain of what you will see when we do 1 on the computer. This test was done on~~ a ~~computer~~ that ~~was not working as it should, running at slow speed and having certain issues~~ with ~~freezing up.<br><br>Google Chrome crashes on Windows 7 by~~ the ~~corrupted cache contents~~ and ~~issues with~~ the ~~stored browsing information~~. ~~Delete~~ the ~~browsing information and well-defined the contents of the cache to resolve this issue.~~<br><br>~~With~~ the ~~Internet,~~ the ~~danger to~~ the ~~registry~~ is ~~more and windows XP error messages might appear frequently~~. ~~Why?~~ The ~~malicious wares like viruses~~, ~~Trojans~~, ~~spy-wares~~, ~~ad wares~~, ~~plus the like gets recorded too. Cookies are perfect examples. You reach conserve passwords~~, ~~and stuff~~, ~~right? That is a easy illustration of the register functioning.<br><br>How to fix this problem is to initially reinstall the program~~(s) ~~causing the mistakes. There are a lot of different programs which use this file~~, ~~however 1 can have placed their own faulty version of the file onto a program. By reinstalling any programs which are causing the error~~, ~~we will not only enable a PC to run the system correctly~~, ~~however a new file is placed onto a system - leaving the computer running as smoothly as possible again. If you try this~~, ~~plus discover it does not function~~, ~~then we should look to update your program & any software you have on a PC~~. ~~This will probably update~~ the ~~Msvcr71.dll file, permitting your computer to read it correctly again.<br><br>There are actually many~~ [~~http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities~~] ~~software pieces inside the internet plus truly the only thing that you want to do is to download them~~. ~~Unfortunately, you cannot expect which all~~ of ~~these are as efficient because they claim to be. And due to this, it is required for you to check~~ when ~~your vendor is really reliable~~ and ~~credible.<br><br>S/w connected error handling - If~~ the ~~blue screen bodily memory dump arises after~~ the ~~installation~~ of ~~s/w application or a driver it might be which there~~ is ~~system incompatibility. By booting into safe mode plus removing~~ the ~~software you are able to rapidly fix this error. We could furthermore try out a "program restore" to revert to~~ an ~~earlier state~~.~~<br><br>Most probably in the event you are experiencing~~ a ~~slow computer it can be a couple years old~~. ~~You also could not have been told that whilst you utilize the computer everyday; there~~ are ~~certain items which it requires to continue running inside its ideal performance~~. ~~We moreover might not even own any diagnostic tools that will get your PC running like hot again. So never allow which stop we from getting the program cleaned. With access~~ to ~~the internet you are able to find the tools which will help we receive your program running like brand-new again~~.~~<br><br>What I would recommend is to look on the own for registry products~~. ~~We can do this with a Google search~~. ~~Whenever you find goods, look~~ for ~~critiques and testimonials about~~ the ~~product~~. ~~Next you can see how others like the product~~, ~~and how perfectly it functions~~.		A '''centered''' (or '''centred''') '''triangular number''' is a [[centered number\|centered]] [[figurate number]] that represents a [[triangle]] with a dot in the center and all other dots surrounding the center in successive triangular layers. The centered triangular number for ''n'' is given by the formula

			<math>{{3n^2 + 3n + 2} \over 2}.</math>

			The following image shows the building of the centered triangular numbers using the associated figures: at each step the previous figure, shown in red, is surrounded by a triangle of new points, in blue.

			[[Image:Construct-nombres-tri-centres.png\|construction]]

			The first few centered triangular numbers are:

			:[[1 (number)\|1]], [[4 (number)\|4]], [[10 (number)\|10]], [[19 (number)\|19]], [[31 (number)\|31]], [[46 (number)\|46]], [[64 (number)\|64]], [[85 (number)\|85]], [[109 (number)\|109]], [[136 (number)\|136]], 166, 199, 235, 274, 316, 361, 409, 460, 514, 571, 631, 694, 760, 829, 901, 976, 1054, 1135, 1219, 1306, 1396, 1489, 1585, 1684, 1786, 1891, 1999, 2110, 2224, 2341, 2461, 2584, 2710, 2839, 2971, … {{OEIS\|id=A005448}}.

			Each centered triangular number from 10 onwards is the sum of three consecutive regular [[triangular number]]s. Also each centered triangular number has a remainder of 1 when divided by three and the quotient (if positive) is the previous regular triangular number.

			The sum of the first ''n'' centered triangular numbers is the [[magic constant]] for an ''n'' by ''n'' normal [[magic square]] for ''n'' > 2.

			== Centered triangular prime ==
			A '''centered triangular prime''' is a centered triangular number that is [[prime number\|prime]]. The first few centered triangular primes are

			:19, 31, 109, 199, 409, … {{OEIS\|id=A125602}}.

			(corresponding to n: 3, 4, 8, 11, 16, ...)

			==References==
			*[[Lancelot Hogben]]: ''Mathematics for the Million''.(1936), republished by W. W. Norton & Company (September 1993), ISBN 978-0-393-31071-9
			*{{MathWorld\|urlname=CenteredTriangularNumber\|title=Centered Triangular Number}}

			{{Classes of natural numbers}}

			[[Category:Figurate numbers]]

en>CRGreathouse: +cat

2012-03-19T16:57:27Z

+cat

New page

Let's look an actual registry scan plus certain of what you will see when we do 1 on the computer. This test was done on a computer that was not working as it should, running at slow speed and having certain issues with freezing up. Google Chrome crashes on Windows 7 by the corrupted cache contents and issues with the stored browsing information. Delete the browsing information and well-defined the contents of the cache to resolve this issue. With the Internet, the danger to the registry is more and windows XP error messages might appear frequently. Why? The malicious wares like viruses, Trojans, spy-wares, ad wares, plus the like gets recorded too. Cookies are perfect examples. You reach conserve passwords, and stuff, right? That is a easy illustration of the register functioning. How to fix this problem is to initially reinstall the program(s) causing the mistakes. There are a lot of different programs which use this file, however 1 can have placed their own faulty version of the file onto a program. By reinstalling any programs which are causing the error, we will not only enable a PC to run the system correctly, however a new file is placed onto a system - leaving the computer running as smoothly as possible again. If you try this, plus discover it does not function, then we should look to update your program & any software you have on a PC. This will probably update the Msvcr71.dll file, permitting your computer to read it correctly again. There are actually many [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities] software pieces inside the internet plus truly the only thing that you want to do is to download them. Unfortunately, you cannot expect which all of these are as efficient because they claim to be. And due to this, it is required for you to check when your vendor is really reliable and credible. S/w connected error handling - If the blue screen bodily memory dump arises after the installation of s/w application or a driver it might be which there is system incompatibility. By booting into safe mode plus removing the software you are able to rapidly fix this error. We could furthermore try out a "program restore" to revert to an earlier state. Most probably in the event you are experiencing a slow computer it can be a couple years old. You also could not have been told that whilst you utilize the computer everyday; there are certain items which it requires to continue running inside its ideal performance. We moreover might not even own any diagnostic tools that will get your PC running like hot again. So never allow which stop we from getting the program cleaned. With access to the internet you are able to find the tools which will help we receive your program running like brand-new again. What I would recommend is to look on the own for registry products. We can do this with a Google search. Whenever you find goods, look for critiques and testimonials about the product. Next you can see how others like the product, and how perfectly it functions.