# Difference between revisions of "Saouter number"

(cat) |
(refs) |
||

Line 1: | Line 1: | ||

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>. |

− | |||

− | |||

− | |||

− | |||

==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]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]}.