: Mathématiques: Riesel number

mathematical analysis > calculus > sequence > integer sequence > Riesel number

number > natural numbers > Riesel number

number > number theory > analytic number theory > Riesel number

Riesel number

In mathematics, a Riesel number is an odd natural number k for which ${\\displaystyle k\ imes 2^{n}-1}$ is composite for all natural numbers n (sequence A101036 in the OEIS). In other words, when k is a Riesel number, all members of the following set are composite:
${\\displaystyle \\left\\{\\,k\ imes 2^{n}-1:n\\in \\mathbb {N} \\,\ ight\\}.}$
If the form is instead ${\\displaystyle k\ imes 2^{n}+1}$ , then k is a Sierpinski number.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riesel_number)