[seqfan] Re: A260119; Least positive integer k such that 2^n-1 and k^n-1 are relatively prime.

Bob Selcoe rselcoe at entouchonline.net
Wed Sep 2 08:57:22 CEST 2015


Hi David,

I'm a bit confused about your conjectured list up to n=5000.  Why, for 
example, do you conjecture that m=9 when n=72, m=1 when n=126, and m=5 when 
n=128?  Why are these upperbounds?

Any idea how to calculate m?  The pattern seems quite irregular.

Best Wishes,
Bob Selcoe

--------------------------------------------------
From: "David Corneth" <davidacorneth at gmail.com>
Sent: Tuesday, September 01, 2015 2:13 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] A260119; Least positive integer k such that 2^n-1 and 
k^n-1 are relatively prime.

> So I've put a conjecture that might help finding such values of k, but I
> don't see a proof and I guess a faster program could be found. There are
> some examples to it, but I don't know what characteristic these n have. 
> The
> conjecture is in the history of the sequence, see
> https://oeis.org/history/view?seq=A260119&v=36
>
> Any ideas on how to proceed?
>
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> Seqfan Mailing list - http://list.seqfan.eu/
> 


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