The primitive divisors of A002450 are listed in A129735 (along with a reference to Zsigi) Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Thu, Jul 23, 2015 at 8:41 AM, Victor S. Miller <victorsmiller@gmail.com> wrote:
These are called primitive divisors. There's a theorem of Zsigismondy which covers this . See this paper for details: http://www.uea.ac.uk/~h008/research/primes.pdf
Victor
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On Jul 22, 2015, at 18:22, Dan Asimov <asimov@msri.org> wrote:
Consider the sequence s_n := (4^n-1)/3, n = 1,2,3,....
Back of the envelope shows that at least for very low n, s_n is squarefree and always has a prime factor that's not a factor of any previous s_n.
Do these patterns continue forever, and if so, why?
This is OEIS A002450 <https://oeis.org/A002450>, but these features are not mentioned there — so it seems likely they're both false.
—Dan
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