[seqfan] Re: More (composite) terms for A233281. Was: Is Fibo(p) always squarefree?

Susanne Wienand susanne.wienand at gmail.com
Mon Feb 3 09:30:06 CET 2014


Hello Antti,

I got a(624) = 75077 and that F_97 is the least Fibonacci number which is a
multiple of 75077.

75077 = 193*389
F_97 / 75077 = 83621143489848422977 / 75077 =  1113805073322701.

Regards
Susanne



2014-02-02 Alonso Del Arte <alonso.delarte at gmail.com>:

> For me, it was actually Ralf's question on A037917 that got me interested
> in the question of mu(F(p)).
>
> Al
>
>
> On Sat, Feb 1, 2014 at 9:08 PM, Antti Karttunen
> <antti.karttunen at gmail.com>wrote:
>
> > On Sun, Feb 2, 2014 at 4:01 AM, Antti Karttunen
> > <antti.karttunen at gmail.com> wrote:
> > > Excuse me,
> > >
> > > but seeing that the topic was at least tangentially about A001177
> > > (Fibonacci entry points), I wonder, is there anybody who (with his/her
> > > desktop super-computer) could search for more composite terms in:
> > > http://oeis.org/A233281 that I recently submitted: "Numbers n such
> > > that A001177(n) is prime."
> > > So far, only two composites there, 4181 and 10877, are known.
> > >
> > > Also, another idea: If we collect a subset from
> > > http://oeis.org/A061488 the primitive prime factors, but only for the
> > > composite Fibonacci numbers, we should get:
> > > 3,7,17,11,29,61,...
> > > (Not yet in OEIS, but warning: my hand/head-calculation at 3:50 am
> local
> > time).
> >
> > Actually, use:
> > http://oeis.org/A061446
> > E.g. A061446(19) = 4181 = 37*113, both should be included at that
> > point, not just 37 as in A061448.
> >
> >
> > > "Primitive prime divisors of fibonacci(c) with c composite, ordered by
> > c".
> > > which I think should be a complementary subset (among primes)
> > > to http://oeis.org/A092395 "Primes occurring as divisors of
> > > fibonacci(p) with p prime." ?
> > >
> > >
> > > Yours,
> > >
> > > Antti Karttunen
> > >
> > >
> > >>
> > >> Message: 7
> > >> Date: Tue, 28 Jan 2014 14:40:49 -0500
> > >> From: Charles Greathouse <charles.greathouse at case.edu>
> > >> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > >> Subject: [seqfan] Re: Is F(p) always squarefree?
> > >> Message-ID:
> > >>         <
> > CAAkfSGLwO4e434QS8fwqA0SL4M8n1aeOtBAZCyhre8Ed6bZLDg at mail.gmail.com>
> > >> Content-Type: text/plain; charset=ISO-8859-1
> > >>
> > >> Suppose F_n is divisible by k^2. Then n is divisible by A001177(k^2) =
> > >> A132632(k). So a necessary condition for F_p being squarefree is that
> > >> A132632(q) is prime for some prime q. But this can happen only when
> > Wall's
> > >> conjecture fails, so if F_p is not squarefree than it is divisible by
> > the
> > >> square of a Wall-Sun-Sun prime. (Right?) I think current expectations
> > are
> > >> that infinitely many Wall-Sun-Sun primes exist, but they should have
> > only
> > >> doubly-logarithmic density and so it seems very hard to find any and
> > >> near-impossible to find more than one.
> > >>
> > >> Charles Greathouse
> > >> Analyst/Programmer
> > >> Case Western Reserve University
> > >>
> > >>
> > >> On Tue, Jan 28, 2014 at 2:17 PM, Alonso Del Arte
> > >> <alonso.delarte at gmail.com>wrote:
> > >>
> > >>> Given a prime p, the number Fibonacci(p) might be composite, but, at
> > least
> > >>> for small p, appears to always be squarefree. This seems like
> something
> > >>> that could easily be proven one way or the other with something in
> > Koshy's
> > >>> book, but the Library is closed today.
> > >>>
> > >>> Al
> > >>>
> > >>> --
> > >>> Alonso del Arte
> > >>> Author at SmashWords.com<
> > >>> https://www.smashwords.com/profile/view/AlonsoDelarte>
> > >>> Musician at ReverbNation.com <
> > http://www.reverbnation.com/alonsodelarte>
> > >>>
> > >>> _______________________________________________
> > >>>
> > >>> Seqfan Mailing list - http://list.seqfan.eu/
> > >>>
> > >>
> > >>
> > >> ------------------------------
> > >>
> > >> Message: 8
> > >> Date: Tue, 28 Jan 2014 12:12:44 -0800
> > >> From: "T. D. Noe" <noe at sspectra.com>
> > >> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > >> Subject: [seqfan] Re: Is F(p) always squarefree?
> > >> Message-ID: <p06240808cf0dbf0b404a@[192.168.1.2]>
> > >> Content-Type: text/plain; charset="us-ascii"
> > >>
> > >> There is a paper "The Fibonacci sequence module p^2 - An investigation
> > by
> > >> computer for p < 10^14" by Elsenhans and Jahnel.  See
> > >> http://www.uni-math.gwdg.de/tschinkel/gauss/Fibon.pdf
> > >>
> > >> Best regards,
> > >>
> > >> Tony
> > >>
> > >> At 2:17 PM -0500 1/28/14, Alonso Del Arte wrote:
> > >>>Given a prime p, the number Fibonacci(p) might be composite, but, at
> > least
> > >>>for small p, appears to always be squarefree. This seems like
> something
> > >>>that could easily be proven one way or the other with something in
> > Koshy's
> > >>>book, but the Library is closed today.
> > >>>
> > >>>Al
> > >>>
> > >>>--
> > >>>Alonso del Arte
> > >>>Author at
> > >>>SmashWords.com<https://www.smashwords.com/profile/view/AlonsoDelarte>
> > >>>Musician at ReverbNation.com <
> http://www.reverbnation.com/alonsodelarte
> > >
> > >>>
> > >>>_______________________________________________
> > >>>
> > >>>Seqfan Mailing list - http://list.seqfan.eu/
> > >>
> > >>
> > >>
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
>
> --
> Alonso del Arte
> Author at SmashWords.com<
> https://www.smashwords.com/profile/view/AlonsoDelarte>
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


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