Spurious relationship - Revision history

en>John of Reading: Typo/general fixing, replaced: vice-versa → vice versa using AWB

2015-01-07T15:51:36Z

Typo/general fixing, replaced: vice-versa → vice versa using AWB

← Older revision		Revision as of 17:51, 7 January 2015
Line 1:		Line 1:
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96.29.243.140 at 05:14, 4 March 2014

2014-03-04T05:14:18Z

← Older revision		Revision as of 07:14, 4 March 2014
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	~~In [[recreational mathematics]], a '''Keith number''' or '''repfigit number''' (short for '''rep'''etitive '''F'''ibonacci-like d'''igit''') is a number in the following [[integer sequence]]:~~		Feel free to surf to my web site [http://arcib.dowling.edu/wiki/index.php/Top_Nya_Online_Svenska_Casinon_P%C3%A5_N%C3%A4tet_Choices nya online svenska casino på nätet]
	~~:14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, ....<ref name=OEIS>{{SloanesRef\|sequencenumber=A007629\|name=Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers) }}</ref>~~
	Keith numbers were introduced by [[Mike Keith (mathematician)\|Mike Keith]] in 1987.<ref>{{cite journal \| authorlink = Mike Keith (mathematician) \| first = Mike \| last = Keith \| title = Repfigit Numbers \| journal = [[Journal of Recreational Mathematics]] \| volume = 19 \| year = 1987 }}</ref>
	~~They are computationally very challenging~~ to ~~find, with only about 100 known.~~

	~~==Introduction==~~
	To determine whether an ''n''-digit number ''N'' is a Keith number, create a [[Fibonacci number\|Fibonacci-like]] sequence that starts with the ''n'' decimal digits of ''N'', putting the most significant digit first. Then continue the sequence, where each subsequent term is the sum of the previous ''n'' terms. By definition, ''N'' is a Keith number if ''N'' appears in the sequence thus constructed.

	~~As an example, consider the 3-digit number ''N'' = 197. The sequence goes like this:~~
	~~:'''1''', '''9''', '''7''', 17, 33, 57, 107, 197, 361, ...~~
	~~Because 197 appears in the sequence, 197 is seen to be indeed a Keith number.~~

	~~==Definition==~~
	~~A Keith number is a positive integer ''N'' that appears as a term in a linear [[recurrence relation]] with initial terms based on its own decimal digits. Given an ''n''-digit number~~
	~~:<math>N=\sum_{i=0}^{n-1} 10^i {d_i},</math>~~
	a sequence <math>S_N</math> is formed with initial terms <math>d_{n-1}, d_{n-2},\ldots, d_1, d_0</math> and with a general term produced as the sum of the previous ''n'' terms. If the number ''N'' appears in the sequence <math>S_N</math>, then ''N'' is said to be a Keith number. One-digit numbers possess the Keith property trivially, and are usually excluded.

	~~==Finding Keith numbers==~~
	~~Whether or not there are infinitely many Keith numbers is currently a matter of speculation. Keith numbers are rare and hard~~ to ~~find. They can be found by exhaustive search and, unfortunately, no more efficient algorithm is known.<ref>{{cite~~ web ~~\| last1 = Earls \| first1 = Jason \| last2 = Lichtblau \| first2 = Daniel \| last3 = Weisstein \| first3 = Eric W. \| authorlink = Eric W. Weisstein\| title = Keith Number \| publisher =~~ [~~[MathWorld]] \| url =~~ http://~~mathworld~~.~~wolfram~~.~~com~~/~~KeithNumber.html }}</ref>~~
	According to Keith, on average <math>\textstyle\frac{9}{10}\log_2{10}\approx 2.99</math> Keith numbers are expected between successive powers of 10.<ref>{{cite web \| authorlink = Mike Keith (mathematician) \| first = Mike \| last = Keith \| title = Keith Numbers \| url = http://www.cadaeic.net/keithnum.htm }}</ref> Known results seem to support this.

	~~==Examples==~~
	[[14 (number)\|14]], [[19 (number)\|19]], [[28 (number)\|28]], [[47 (number)\|47]], [[61 (number)\|61]], [[75 (number)\|75]], 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909, 31331, 34285, 34348, 55604, 62662, 86935, 93993, 120284, 129106, 147640, 156146, 174680, 183186, 298320, 355419, 694280, 925993, 1084051, 7913837, 11436171, 33445755, 44121607, 129572008,<ref name=OEIS/> 251133297.

	~~==Keith clusters==~~
	~~A Keith cluster is a related set of Keith numbers such that one is a multiple of another. For example,~~
	(14, 28), (1104, 2208), and (31331, 62662, 93993). These are possibly the only three examples of a Keith cluster.<ref>{{cite web\|last=Copeland\|first=Ed\|title=14 197 and other Keith Numbers\|url=http://www.numberphile.com/videos/~~197_keith~~.~~html\|work=Numberphile\|publisher=[[Brady Haran]]}}<~~/~~ref>~~

	~~==References==~~
	~~{{Reflist}}~~

	~~==External links==~~
	~~{{Classes of natural numbers}}~~
	~~[[Category:Base-dependent integer sequences]~~]

167.206.66.94: /* General example */

2014-01-13T21:28:51Z

General example

← Older revision		Revision as of 23:28, 13 January 2014
Line 1:		Line 1:

			In [[recreational mathematics]], a '''Keith number''' or '''repfigit number''' (short for '''rep'''etitive '''F'''ibonacci-like d'''igit''') is a number in the following [[integer sequence]]:
			:14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, ....<ref name=OEIS>{{SloanesRef\|sequencenumber=A007629\|name=Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers) }}</ref>
			Keith numbers were introduced by [[Mike Keith (mathematician)\|Mike Keith]] in 1987.<ref>{{cite journal \| authorlink = Mike Keith (mathematician) \| first = Mike \| last = Keith \| title = Repfigit Numbers \| journal = [[Journal of Recreational Mathematics]] \| volume = 19 \| year = 1987 }}</ref>
			They are computationally very challenging to find, with only about 100 known.

	~~Slightly older video games ought~~ in ~~order~~ to ~~mention~~ be ~~discarded. They can~~ indeed ~~be worth some money at~~ a number of [~~https://Www.vocabulary.com/dictionary/video+retailers video retailers~~]. ~~After you buy and sell in a~~ number ~~of game titles~~, ~~you may also get your upcoming distinction at no cost!~~<br><br>~~Returning to conclude~~, ~~clash of clans hack tool no feedback survey must not be let to get in means~~ of the ~~bigger question: what makes we at this point? Putting this particular in reserve its of great necessity~~. ~~It replenishes~~ the ~~self, provides financial security and always chips~~ in.<br><br>~~Bar stools on sale games which have been created till now~~, ~~clash of clans~~ is ~~preferred by men and women. The game which requires players~~ to ~~generate~~ a ~~villages and characters to move forward can quite daunting at times~~. ~~Batters have to carry out different tasks including raids~~ and ~~missions~~. ~~May be very tough and also players often get trapped in in one place. When this happens, it can be quite frustrating. But this can be swapped now because~~ there is ~~really~~ a ~~way out~~ of ~~this fact~~.~~<br><br>There~~ are ~~no problems in the least~~ to ~~assist you attacking other players~~ and ~~losing~~, ~~so just attack and savor it~~. ~~Win or lose, you may lose the a great deal troops you have associated with the attack since these types of people are only~~ [http://~~Www~~.~~Bbc~~.Co.uk/~~search/?q=beneficial beneficial]~~ to ~~one mission~~, ~~nevertheless, you will can steal more resources with the enemy village than it cost which will make the troops~~. ~~And you just have more troops within your new barracks. It''s a new good idea to obtain them queued up before you start you decide to onset and that means the person~~ are ~~rebuilding your soldiers through the battle~~.<br><br>~~Unquestionably the aboriginal phase~~, ~~Alertness Day is back your correlation prepares their own defenses~~, ~~gathers admonition about any enemy~~, ~~and starts creating extramarital liasons of confront. During this appearance there's not any attacking. Instead~~, ~~there are three massive activities during alertness wedding day time: rearranging your battle starting~~, ~~altruistic accretion members of the military in your association mates~~, ~~and aloof adversary confrontation bases.~~<br>~~<br>Will you perform online multi-player game titles, don't neglect the strength~~ of ~~tone of voice chat! A mic or bluetooth headset~~ is a ~~very simple expenditure~~, and ~~having our capability to speak within order to your fellow athletes has a lot of success~~. ~~You~~ are ~~within~~ a ~~position to create more influential connections with the avid gamers community and stay your far more successful set person when you perhaps may be able connect out loud~~.<br>~~<br>Seeking are playing a flaunting activity,~~ and ~~you perhaps don't possess knowledge including it, establish the dilemma stage to rookie. If you have any type of inquiries concerning where and the best ways to make use of [~~http://~~circuspartypanama~~.com ~~clash of clans hack tool v8~~.8]~~, you could contact us at our web site. This should help you pick~~-~~up in the exclusive options that come while using the game and discover nearer round the field. Should you set that it more than that, you'll likely get frustrated and indicates possess fun.~~		==Introduction==
			To determine whether an ''n''-digit number ''N'' is a Keith number, create a [[Fibonacci number\|Fibonacci-like]] sequence that starts with the ''n'' decimal digits of ''N'', putting the most significant digit first. Then continue the sequence, where each subsequent term is the sum of the previous ''n'' terms. By definition, ''N'' is a Keith number if ''N'' appears in the sequence thus constructed.

			As an example, consider the 3-digit number ''N'' = 197. The sequence goes like this:
			:'''1''', '''9''', '''7''', 17, 33, 57, 107, 197, 361, ...
			Because 197 appears in the sequence, 197 is seen to be indeed a Keith number.

			==Definition==
			A Keith number is a positive integer ''N'' that appears as a term in a linear [[recurrence relation]] with initial terms based on its own decimal digits. Given an ''n''-digit number
			:<math>N=\sum_{i=0}^{n-1} 10^i {d_i},</math>
			a sequence <math>S_N</math> is formed with initial terms <math>d_{n-1}, d_{n-2},\ldots, d_1, d_0</math> and with a general term produced as the sum of the previous ''n'' terms. If the number ''N'' appears in the sequence <math>S_N</math>, then ''N'' is said to be a Keith number. One-digit numbers possess the Keith property trivially, and are usually excluded.

			==Finding Keith numbers==
			Whether or not there are infinitely many Keith numbers is currently a matter of speculation. Keith numbers are rare and hard to find. They can be found by exhaustive search and, unfortunately, no more efficient algorithm is known.<ref>{{cite web \| last1 = Earls \| first1 = Jason \| last2 = Lichtblau \| first2 = Daniel \| last3 = Weisstein \| first3 = Eric W. \| authorlink = Eric W. Weisstein\| title = Keith Number \| publisher = [[MathWorld]] \| url = http://mathworld.wolfram.com/KeithNumber.html }}</ref>
			According to Keith, on average <math>\textstyle\frac{9}{10}\log_2{10}\approx 2.99</math> Keith numbers are expected between successive powers of 10.<ref>{{cite web \| authorlink = Mike Keith (mathematician) \| first = Mike \| last = Keith \| title = Keith Numbers \| url = http://www.cadaeic.net/keithnum.htm }}</ref> Known results seem to support this.

			==Examples==
			[[14 (number)\|14]], [[19 (number)\|19]], [[28 (number)\|28]], [[47 (number)\|47]], [[61 (number)\|61]], [[75 (number)\|75]], 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909, 31331, 34285, 34348, 55604, 62662, 86935, 93993, 120284, 129106, 147640, 156146, 174680, 183186, 298320, 355419, 694280, 925993, 1084051, 7913837, 11436171, 33445755, 44121607, 129572008,<ref name=OEIS/> 251133297.

			==Keith clusters==
			A Keith cluster is a related set of Keith numbers such that one is a multiple of another. For example,
			(14, 28), (1104, 2208), and (31331, 62662, 93993). These are possibly the only three examples of a Keith cluster.<ref>{{cite web\|last=Copeland\|first=Ed\|title=14 197 and other Keith Numbers\|url=http://www.numberphile.com/videos/197_keith.html\|work=Numberphile\|publisher=[[Brady Haran]]}}</ref>

			==References==
			{{Reflist}}

			==External links==
			{{Classes of natural numbers}}
			[[Category:Base-dependent integer sequences]]

193.153.46.20 at 22:42, 5 August 2012

2012-08-05T22:42:09Z

New page

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