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

[Alonso Del Arte]

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/
> >>
> >>
> >>
>
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>
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>



-- 
Alonso del Arte
Author at SmashWords.com<https://www.smashwords.com/profile/view/AlonsoDelarte>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>