[seqfan] Re: Integers k of the form (2^m + 1) / (2^n + 1)

[Neil Sloane]

Too late, I already recycled A370377.  The A-number will have been reused
by now.  Can you reconstruct it with a new A-number, and tell me what it
is.  Then I will modify the Wiki page of Deleted Sequences to indicate that
it has been renumbered, not recycled.

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com



On Sun, Feb 18, 2024 at 10:50 AM Max Alekseyev <maxale at gmail.com> wrote:

> Oh, I see the issue now - https://oeis.org/A079665 is sorted as an
> irregular triangular array.
> Row s contains numbers corresponding to suitable r (co-divisors to odd
> divisors of s).
> Number 1 may or may not be included in each row (we can leave it out to
> keep it more consistent with the current data).
> I will clarify the definition of A079665.
>
> And I take back my suggestion to discard A370377 - sorry for confusion.
>
> Regards,
> Max
>
>
> On Sun, Feb 18, 2024 at 10:33 AM Neil Sloane <njasloane at gmail.com> wrote:
>
> > I followed Max's suggestion
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, Chairman, OEIS Foundation.
> > Also Visiting Scientist, Math. Dept., Rutgers University,
> > Email: njasloane at gmail.com
> >
> >
> >
> > On Sun, Feb 18, 2024 at 10:23 AM Max Alekseyev <maxale at gmail.com> wrote:
> >
> > > Sequence of such numbers is already present as
> https://oeis.org/A079665
> > > which however rather artificially excludes number 1.
> > > I'd suggest relaxing the definition of https://oeis.org/A079665 to
> > include
> > > 1, and discard the draft of A370377.
> > >
> > > Regards,
> > > Max
> > >
> > > On Sat, Feb 17, 2024 at 2:09 AM Tomasz Ordowski <
> > tomaszordowski at gmail.com>
> > > wrote:
> > >
> > > > Dear Sequence Fans!
> > > >
> > > > The numbers k > 0 for which the equation
> > > > 2^m + k = k*2^n + 1 has a solution m,n > 0
> > > > are integers of the form (2^m - 1) / (2^n - 1),
> > > > i.e. if an only if n divides m. I wrote about it.
> > > > See https://oeis.org/A064896 (my comment).
> > > > Primes of the sequence A064896 are A245730.
> > > > See https://oeis.org/A245730 (all these primes).
> > > > Contains: all Mersenne primes, all Fermat primes,
> > > > and other primes {73, 262657, 4432676798593, ...}.
> > > >    Contrary to appearances, a sufficiently large number k of this
> form
> > > > cannot be a dual Sierpinski number, but may be a dual Riesel number.
> > > >
> > > > The numbers k for which the equation
> > > > 2^m - k = k*2^n - 1 has a solution m,n > 0
> > > > are integers of the form (2^m + 1) / (2^n + 1).
> > > > Note that if 2^n+1 divides 2^m+1, then n divides m.
> > > > 1, 3, 11, 13, 43, 57, 171, 205, 241, 683, 993, 2731, 3277, ...
> > > > This important sequence is not found on the OEIS websites.*
> > > > Something related. See A281728 for primes in this sequence:
> > > > https://oeis.org/A281728 (unfortunately, without definition there).
> > > > Question: are these exactly primes of the form (2^m+1)/(2^n+1)?
> > > >     Appearances are deceiving again,
> > > > because a sufficiently large number k of this form
> > > > cannot be a dual Riesel number, but may be a dual Sierpinski number.
> > > >
> > > > Best,
> > > >
> > > > Tom Ordo
> > > > _________________
> > > > (*) See my new draft: https://oeis.org/draft/A370377
> > > > https://oeis.org/A076336 (Sierpinski numbers).
> > > > https://oeis.org/A101036 (Riesel numbers).
> > > >
> > > > --
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> > > >
> > >
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