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• Hi all! I recently got interested on Sierpinki s Theorem: Consider the sequence S_k={2^n·k+1} where k is a fixed positive integer. Then there exist infinitely
Message 1 of 3 , Jun 6, 2013
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Hi all!

I recently got interested on Sierpinki's Theorem: Consider the sequence
S_k={2^n·k+1} where k is a fixed positive integer. Then there exist
infinitely many k's such that S_k contains no primes.

I wonder about generalizations and related results:

a) What if we ask for 3^n·k+1 or more generally, for a "base" b^n·k+1?

b) Can a number be Sierpinski for several different bases b simultaneously?

c) Can a number be Sierpinski and Riesel at the same time? (Recall that
Riesel numbers are as Sierpinski but with the general formula 2^n·k-1).

d) What can be said about S_k when k is NOT Sierpinski? Does it have
infinitely many primes, or can it have a finite nonzero number of them?

I hope that some of you have a (maybe partial) answer to any of these
questions!

Kindest regards,
Jose Brox

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• ... What if we ask for 3^n·k+1 or more generally, for a base b^n·k+1? http://www.mersenneforum.org/showthread.php?t=9738 David
Message 2 of 3 , Jun 7, 2013
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--- In primenumbers@yahoogroups.com, Jose Ramón Brox <ambroxius@...> wrote:

What if we ask for 3^n·k+1 or more generally, for a "base" b^n·k+1?

David
• Thank you both for the info! Jose 2013/6/7 djbroadhurst ... -- La verdad (blog de raciocinio político e información
Message 3 of 3 , Jun 7, 2013
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Thank you both for the info!

Jose

> **
>
>
>
>
> --- In primenumbers@yahoogroups.com, Jose Ram�n Brox <ambroxius@...>
> wrote:
>
> What if we ask for 3^n�k+1 or more generally, for a "base" b^n�k+1?
>
>
> David
>
>
>

--
La verdad (blog de raciocinio pol�tico e informaci�n
social)<http://josebrox.blogspot.com/>

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