[seqfan] Re: All the metal mean sequence primes.

[Jess Tauber]

This is a bit off to the side of the strict topic- but I was playing with
Pell numbers tonight myself (related to the Silver Mean) with regard to
trying to reverse engineer a kind of multi-tier generalized Pascal Triangle
analogue. Since in the Silver Mean generalized Pell numbers we double the
following term and add to single copies of the preceding, I thought perhaps
creating TWO triangles might work, joined at the edges, where the single
preceding terms might go. This is as far as I could get (where is Daniel
Jackson when you need him?), since I still have to create the rows and
diagonals within each such that the shallow diagonal values sum to the Pell
numbers. Does anyone know of any work in this area?

Jess Tauber


On Thu, Aug 1, 2013 at 1:36 PM, Neil Sloane <njasloane at gmail.com> wrote:

> Dan's sequence seems not to have made it into the OEIS, so I have added it:
> see A227829.
> Hans, could you add the further terms you found?
> Dan, could you replace "DAN CYN J" in the entry with your real name?
> Thanks
> Neil
>
>
> On Sun, Jul 21, 2013 at 11:42 PM, Hans Havermann <gladhobo at teksavvy.com
> >wrote:
>
> > Dan has explained to me that he meant the sequences:
> >
> > 2, 3, 5, ..
> > 5, 12, 29, ..
> > 10, 33, 109, ..
> > 17, 72, 305, ..
> > etc.
> >
> > a(n) = m*a(n-1) + a(n-2), where a(1) = 1, a(2) = positive integer m, and
> > n>2.
> >
> > I confirmed his prime collection and added a few more terms.
> >
> >
> > I had written:
> >
> > > On Jul 19, 2013, at 10:35 PM, DAN_CYN_J <dan_cyn_j at comcast.net> wrote:
> > >
> > >> Where the first term generator = (1) for each sequence.
> > >> Then the second term generator integer = (1,2,3,4,5,6,7...in order for
> > each sequence.)
> > >>
> > >> All primes that appear in these sequence's after the second term
> > >> up to 1601 are listed below.
> > >>
> > >>
> >
> 2,3,5,13,17,29,37,89,101,109,197,233,257,401,577,677,701,1297,1597,1601--->oo.
> > >
> > >
> > > It isn't at all clear to me what you are enumerating here but my
> > impression is that you are combining all primes found in:
> > >
> > > 2, 3, 5, ..
> > > 3, 5, 8, ..
> > > 4, 7, 11, ..
> > > 5, 9, 14, ..
> > > etc.
> > >
> > > But that can't be right because *all* primes appear.
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
>
> --
> Dear Friends, I have now retired from AT&T. New coordinates:
>
> Neil J. A. Sloane, President, OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
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