# [seqfan] Re: Conway's subprime Fibonacci sequences

Tanya Khovanova tanyakh at yahoo.com
Fri Jul 27 15:42:45 CEST 2012

```The cycle length sequence is conjectured.
We do not have a proof that these are the only cycle lengths, there could be cycle lengths in between. Also, we do not have a proof that there couldn't be two cycles of the same length.

________________________________
From: Wouter Meeussen <wouter.meeussen at telenet.be>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Cc: Julian Salazar <jsalazar01 at college.harvard.edu>
Sent: Friday, July 27, 2012 6:43 AM
Subject: [seqfan] Re: Conway's subprime Fibonacci sequences

Neil, Julian,

would you be ok with the following strategy:

I submit the cycle lengths (1), 10, 11, 18, 19, 56, 136 as 'potentially
finite'
and then, separately,  for each cycle-case, the sequence starting from the
smallest starting pair
~min (a^2+b^2).  (cfr.  Fig 3.)
[[ problem: the 136 cycle might not fit on 3 lines ]]
That makes 6 extra sequences.
Or did I miss something?

Wouter.

-----Original Message-----
From: Neil Sloane
Sent: Thursday, July 26, 2012 5:24 PM
To: Sequence Fanatics Discussion list
Cc: Julian Salazar
Subject: [seqfan] Re: Conway's subprime Fibonacci sequences

Wouter, It looks like none of those sequences are in the OEIS yet - at
least three have been mentioned so far. Would you be kind enough to submit
them all?
Thanks!
Neil

On Tue, Jul 24, 2012 at 1:10 PM, Wouter Meeussen <wouter.meeussen at telenet.be
> wrote:

> let's not all do this simultaneously.
> I'm ready & willing to oblige, anyone else busy on it right now?
>
> Wouter.
>
> -----Original Message----- From: Neil Sloane Sent: Tuesday, July 24, 2012
> 5:00 PM To: Sequence Fanatics Discussion list Cc: Julian Salazar Subject:
> [seqfan] Re: Conway's subprime Fibonacci sequences
> Tanya, Richard, Julian:
>
> You should be aware of the paper by Back and Caragiu,
> G. Back and M. Caragiu, The greatest prime factor and recurrent sequences,
> Fib. Q., 48 (2010), 358-362.
> which is closely related. Also sequences A175723, A177904, etc., which are
> based on that paper.
>
> Perhaps Julian could submit the sequence? - I see he is the primary author
> of the ArXiv paper
>
> Neil
>
>
> On Tue, Jul 24, 2012 at 10:26 AM, Tanya Khovanova <
> mathoflove-seqfan at yahoo.com> wrote:
>
>  Dear SeqFans,
>>
>> I just coauthored a paper "Conway's subprime Fibonacci sequences" with
>> Richard K. Guy and Julian Salazar. The paper is in the arxiv:
>> http://arxiv.org/abs/1207.5099
>>
>> The main sequence (starting with 0,1) should be submitted. In July, I am
>> working at RSI and do not have time to breath. Please, submit.
>>
>> The rule is: the next term is the sum of the two previous terms, and, if
>> the sum is composite, it is divided by the least prime factor.
>> Let me illustrate what is going on. First we start with two integers.
>> Let's take 1 and 1 as in the Fibonacci sequence. Then the next term is
>> 2, because it is prime and we do not divide by anything. The next two
>> terms are 3 and 5. After that the sum of two terms is 8, which is now
>> composite and it is divided by 2. So the sequence goes: 1, 1, 2, 3, 5,
>> 4, 3, 7, 5, 6, 11 and so on.
>>
>>
>> Tanya
>>
>> ______________________________**_________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>
>
> --
> Dear Friends, I have now retired from AT&T. New coordinates:
>
> Neil J. A. Sloane, President, OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA
> Email: njasloane at gmail.com
>
> ______________________________**_________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
> ______________________________**_________________
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> Seqfan Mailing list - http://list.seqfan.eu/
>

--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Email: njasloane at gmail.com

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