: Mathématiques: Sierpiński number

mathematical analysis > calculus > sequence > integer sequence > Sierpiński number

number > natural numbers > Sierpiński number

number > number theory > analytic number theory > Sierpiński number

Sierpiński number

In number theory, a Sierpiński number is an odd natural number k such that ${\\displaystyle k\ imes 2^{n}+1}$ is composite for all natural numbers n. In 1960, Wacław Sierpiński proved that there are infinitely many odd integers k which have this property. In other words, when k is a Sierpiński number, all members of the following set are composite:
${\\displaystyle \\left\\{\\,k\\cdot 2^{n}+1:n\\in \\mathbb {N} \\,\ ight\\}.}$
If the form is instead ${\\displaystyle k\ imes 2^{n}-1}$ , then k is a Riesel number.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Sierpi%C5%84ski_number)

http://data.loterre.fr/ark:/67375/PSR-PVX57VVP-X

RDF/XML TURTLE JSON-LD Date de création 26/07/2023, dernière modification le 18/10/2024

Loterre