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.
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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>.
 
 
==External links==
 
*[https://hal.inria.fr/file/index/docid/73966/filename/RR-2728.pdf Paper by Saouter]
 
*[http://tony.reix.free.fr/Mersenne/PropertiesOfFermatLikeTNumbers.pdf More details of this sequence by Tony Reix]
 
  
 
==References==
 
==References==
*Yannick Saouter. A Fermat-Like Sequence and Primes of the Form 2h.3n + 1. [Research Report] RR-2728, INRIA. 1995. inria-00073966
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<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]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 numbers. These numbers were named by Tony Reix[1][2] after Yannick Saouter, who studied these numbers[3].

References