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Difference between revisions of "Saouter number"
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A '''Saouter number''' is a type of [[Generalized Fermat number]]. Numbers of this type have the form | A '''Saouter number''' is a type of [[Generalized Fermat number]]. Numbers of this type have the form | ||
| − | <math>4^{3^n}+2^{3^n}+1</math> | + | <math>A_n = 4^{3^n}+2^{3^n}+1</math> |
| − | In the notation of John Cosgrave, the Saouter numbers are generated by the sequence <math>F_{n,2}</math>. Due to this, these numbers share similar properties to those held by [[Fermat number]]s. These numbers were named by Tony Reix after Yannick Saouter, who studied these numbers | + | In the notation of [[John Cosgrave]], the Saouter numbers are generated by the sequence <math>F_{n,2}</math>. Due to this, these numbers share similar properties to those held by [[Fermat number]]s. These numbers were named by [[Tony Reix]]<ref>[https://www.mersenneforum.org/showpost.php?p=143997&postcount=32 MersenneForum] post from 2008-09-28</ref><ref>[http://tony.reix.free.fr/Mersenne/PropertiesOfFermatLikeTNumbers.pdf T.Reix: "A Fermat-like sequence", 2005]</ref> after [[Yannick Saouter]], who studied these numbers<ref>[https://hal.inria.fr/file/index/docid/73966/filename/RR-2728.pdf Y.Saouter: "A Fermat-Like Sequence and Primes of the Form 2h*3^n+ 1, 1995]</ref>. |
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==References== | ==References== | ||
| − | + | <references /> | |
[[Category:Number]] | [[Category:Number]] | ||
Latest revision as of 07:02, 15 August 2019
A Saouter number is a type of Generalized Fermat number. Numbers of this type have the form
[math]\displaystyle{ A_n = 4^{3^n}+2^{3^n}+1 }[/math]
In the notation of John Cosgrave, the Saouter numbers are generated by the sequence [math]\displaystyle{ F_{n,2} }[/math]. Due to this, these numbers share similar properties to those held by Fermat numbers. These numbers were named by Tony Reix[1][2] after Yannick Saouter, who studied these numbers[3].
