Re: [SeqFan] Abridged summary of seqfan@googlegroups.com - 11 updates in 3 topics

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George Whale

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Aug 13, 2026, 7:20:51 AM (14 days ago) Aug 13
to seq...@googlegroups.com
It is interesting, thanks.

George W.

On Thu, 13 Aug 2026, 12:09 , <seq...@googlegroups.com> wrote:
Drumețul Dacic <tri...@gmail.com>: Aug 12 02:31PM +0300

Interesting question!
 
Here is some data for the problem: values of n, for which lambda(2^n - 1)+1
is prime:
 
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, ...more
DONG HAOXUAN <donghaoxuan...@gmail.com>: Aug 12 12:02PM

Hi Tom,
 
I continued playing with this and found a fun one: n = 729 also works.
 
C(729) = lambda(2^729 - 1) + 1
 
is a 174-digit prime. I also verified its primality with a Pocklington ...more
Tomasz Ordowski <tomaszo...@gmail.com>: Aug 12 10:00PM +0200

Thanks for participating in the discussion so far. I really appreciate it.
 
Let a(n) = lambda(2^n - 1) + 1. Finally, one more question to consider:
Are there only finitely many pairs m,n such that ...more
DONG HAOXUAN <donghaoxuan...@gmail.com>: Aug 12 04:21PM -0700

Hi Tom,
 
A quick update from my side — I’ve kept working on the problem and
there has been quite a bit of progress, although I still don’t have a
proof of infinitude yet.
 ...more
Tomasz Ordowski <tomaszo...@gmail.com>: Aug 13 10:24AM +0200

PS. Try also: lambda(2^n + 1) + 1.
Does it give more prime numbers?
 
śr., 12 sie 2026 o 22:00 Tomasz Ordowski <tomaszo...@gmail.com>
napisał(a):
 
 ...more
DONG HAOXUAN <donghaoxuan...@gmail.com>: Aug 13 06:33PM +1000

Yeah sure, I'm currently looking for a solution, but haven't made any
significant progress yet. And thank you for your suggestion; I'll give it a
try.
 
On Thu, Aug 13, 2026 at 6:24 PM Tomasz ...more
Ed Pegg <edp...@gmail.com>: Aug 12 02:38PM -0500

Here's my updated copy of all solutions. Anything I should change before
replacing the current OEIS text file?
 
 ...more
Dave Consiglio <dave...@gmail.com>: Aug 12 02:30PM -0600

Hi Ed,
 
I am running some code on my end on the same problem. a(19) is confirmed
117. My sample set is:
 
[0, 1, 2, 3, 6, 10, 14, 18, 22, 26, 30, 33, 34, 35, 36, 72, 75, 78, 81]
 
 ...more
Ed Pegg <edp...@gmail.com>: Aug 12 06:21PM -0500

Here's my code.... a program called Scrunch was used for sparse rulers, so
I modified it to do sums instead of differences.
 
It can verify the 129 result in about an hour.
 
 ...more
Dave Consiglio <dave...@gmail.com>: Aug 12 06:46PM -0600

Awesome! Thank you for sharing. Mine will finish nowhere near that fast,
but I'll keep it running to ensure I get the same answer.
 
Seems like you should be able to get a(20) and maybe even a(21)! ...more
Bob Lyons <bobly...@gmail.com>: Aug 12 07:24PM -0400

I just stumbled into this page, which may be of interest to SeqFan members. I apologize if it’s old news.
 
https://community.wolfram.com/groups/-/m/t/3778606
 
Bob
 ...more
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