[seqfan] Re: A conjecture of Saha and Karthik.

Alonso Del Arte alonso.delarte at gmail.com
Thu Feb 13 18:01:00 CET 2014


I say yes, you should add it. As a keyword:bref sequence, 6, 12 would be
pretty useless. This way, at least a search for Saha and Karthik would
bring up this conjecture.

Al


On Thu, Feb 13, 2014 at 9:11 AM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> Perhaps the sequence could be
>
> %N Pisano period of n^2 divided by Pisano period of n.
> %S 1, 2, 3, 4, 5, 1, 7, 8, 9, 5, 11, 1, 13, 7, 15, 16, 17, 9, 19, 10, 21,
> 11, 23, 4, 25, 13, 27, 7, 29, 5, 31, 32, 33, 17, 35, 9, 37, 19, 39, 40, 41,
> 7, 43, 44, 45, 23, 47, 16, 49, 25, 17, 26, 53, 27, 55, 14, 19, 29, 59, 5,
> 61, 31, 63, 64, 65, 11, 67, 34, 23, 35, 71, 36, 73, 37, 75, 76, 77, 13, 79,
> 80, 81, 41, 83, 7, 85, 43, 87, 88, 89, 45, 13, 23, 31, 47, 95, 32, 97, 49,
> 99, 50, ...
>
> with the associated conjecture
> %C Conjecture (Saha & Karthik): a(n) = 1 only for n = 1, 6, and 12.
>
> Note also that a(n) | n.
>
> Should I submit this?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
>
> On Wed, Feb 12, 2014 at 8:18 PM, L. Edson Jeffery <lejeffery2 at gmail.com
> >wrote:
>
> > While reading about the Wall-Sun-Sun prime conjecture, I ran across the
> > following conjecture by Saha and Karthik on the last page of their
> preprint
> > http://arxiv.org/abs/1102.1636 :
> >
> >
> > For n a positive integer, let pi(n) denote the least positive integer k
> > such that n | F(k) and F(k+1) == 1 (mod n), where F(m) is the m-th
> > Fibonacci number (pi(n) is sometimes called the 'Pisano period'). Let S
> > denote the set of all solutions of pi(n^2) = pi(n) over the positive
> > integers. Then S = {6,12}.
> >
> >
> > S is reminiscent of the recent A235383 = {8,144}. Is there a deeper
> > relation between the two sequences, and should the conjectured S be
> > included in the database?
> >
> > Ed Jeffery
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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>
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>



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Alonso del Arte
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