en>Sonia.dutta at 16:20, 9 August 2013

2013-08-09T16:20:03Z

← Older revision		Revision as of 18:20, 9 August 2013
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	~~The person who wrote~~ the ~~article~~ is ~~known as Jayson Hirano and he totally digs~~ that ~~title~~. ~~Credit authorising~~ is ~~how he tends to make money. For~~ a ~~while I~~'~~ve been in Alaska but I will have~~ to ~~transfer~~ in ~~a yr or~~ two. ~~What me and my family members love~~ is to ~~climb but I~~'~~m considering on beginning something new~~.<br><br>~~My site~~ ... [http://~~www~~.~~publicpledge~~.~~com~~/~~blogs~~/~~post/7034 best psychic readings~~]		A '''Kynea number''' is an integer of the form

			:<math>4^n + 2^{n + 1} - 1</math>.

			An equivalent formula is

			:<math>(2^n + 1)^2 - 2</math>.

			This indicates that a Kynea number is the ''n''th power of 4 plus the (''n'' + 1)th [[Mersenne number]].
			Kynea numbers were studied by Cletus Emmanuel who named them after a baby girl.<ref>[http://tech.groups.yahoo.com/group/primenumbers/message/14584]</ref>

			The sequence of Kynea numbers starts with:
			: [[7 (number)\|7]], [[23 (number)\|23]], [[79 (number)\|79]], 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407, ... {{OEIS\|id=A093069}}.

			== Properties ==

			The [[Binary numeral system\|binary representation]] of the ''n''th Kynea number is a single leading one, followed by ''n'' - 1 consecutive zeroes, followed by ''n'' + 1 consecutive ones, or to put it algebraically:

			:<math>4^n + \sum_{i = 0}^n 2^i.</math>

			So, for example, 23 is 10111 in binary, 79 is 1001111, etc. The difference between the ''n''th Kynea number and the ''n''th [[Carol number]] is the (''n'' + 2)th [[power of two]].

			== Prime Kynea numbers ==
			Starting with 7, every third Kynea number is a multiple of 7. Thus, for a Kynea number to be a [[prime number]], its index ''n'' can not be of the form 3''x'' + 1 for ''x'' > 0. The first few Kynea numbers that are also prime are 7, 23, 79, 1087, 66047, 263167, 16785407 {{OEIS\|id=A091514}}.

			As of 2006, the largest known prime Kynea number has index ''n'' = 281621 and approximately equals 5.5×10<sup>169552</sup>. It was found by Cletus Emmanuel in November 2005, using ''k''-Sieve from Phil Carmody and OpenPFGW. This is the 46th Kynea prime.


			{{Col-begin}}
			{{Col-1-of-2}}

			{{Col-2-of-2}}
			{{Portal\|Mathematics}}
			{{Col-end}}

			==References==
			<references/>

			==External links==
			* {{MathWorld\|title=Near-Square Prime\|urlname=Near-SquarePrime}}
			* [http://primes.utm.edu/primes/page.php?id=75878 Prime Database entry for Kynea(281621)]

			{{Prime number classes\|state=collapsed}}
			{{Classes of natural numbers}}

			{{DEFAULTSORT:Kynea Number}}
			[[Category:Integer sequences]]

en>Neelix: Fixed link

2011-03-19T20:27:01Z

Fixed link

New page

The person who wrote the article is known as Jayson Hirano and he totally digs that title. Credit authorising is how he tends to make money. For a while I've been in Alaska but I will have to transfer in a yr or two. What me and my family members love is to climb but I'm considering on beginning something new.<br><br>My site ... [http://www.publicpledge.com/blogs/post/7034 best psychic readings]

3char - Revision history

en>Sonia.dutta at 16:20, 9 August 2013

en>Neelix: Fixed link