[seqfan] Re: Q: cyclotomic cosets A006694
Vladimir Shevelev
shevelev at bgu.ac.il
Wed Jan 19 14:00:47 CET 2011
I add the following:
1) A006694(n)=A037226(n) iff 2n+1 is prime;
2) Only case, when A006694(n)<A037226(n) is n=0;
3) If {C_i}. i=1,...,A006694(n), is the set of all cyclotomic cosets of 2 mod (2n+1), then
LCM(|C_1|,...,|C_{A006694(n)}|)=A002326(n).
Regards,
Vladimir
----- Original Message -----
From: Joerg Arndt <arndt at jjj.de>
Date: Tuesday, January 18, 2011 18:17
Subject: [seqfan] Re: Q: cyclotomic cosets A006694
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Now reworded to:
>
> a(n) is not in general the number of orbits in
> (Z/(2n+1)Z)* generated
> by 2, these are counted in A037226. - M. F. Hasler, Jan
> 18 2011.
>
> Hope that's OK.
>
> And yes, some sequences cold benefit from definitions...
>
>
> * Vladimir Shevelev <shevelev at bgu.ac.il> [Jan 18. 2011 17:10]:
> > Yes, when I for the first time have seen this sequence, I did
> not quite understand the definition. Before (up to 2008), I did
> not see term "coset". Besides, I thought that the definition is
> the first statement in Comment: The number of cycles in
> permutations constructed from siteswap juggling patterns 1, 123,
> 12345, 1234567, etc....
> > I did some experiments and posed this conjecture. Later I
> understood that it is the definition and many timis used
> term "coset", but forgot about this my "conjecture"-this word it
> should be removed.
> >
> > Regards,
> > Vladimir
> >
> >
> > ----- Original Message -----
> > From: Joerg Arndt <arndt at jjj.de>
> > Date: Tuesday, January 18, 2011 16:09
> > Subject: [seqfan] Re: Q: cyclotomic cosets A006694
> > To: seqfan at list.seqfan.eu
> >
> > > * Joerg Arndt <arndt at jjj.de> [Jan 18. 2011 15:04]:
> > > > In A006694 there is the comment:
> > > > "Conjecture: a(n) is the number of orbits
> > > > in (Z\(2n+1)Z)* generated by 2."
> > > >
> > > > But that is the definition of the sequence, correct?
> > > > (note to myself: if so, A139035 needs editing as well)
> > > >
> > >
> > > M. F. Hasler took care of that, thanks!
> > >
> > > > [...]
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > Shevelev Vladimir
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
Shevelev Vladimir
More information about the SeqFan
mailing list