A110907

[Ivica Kolar]

Max,
THANK YOU!

Primality was checked here (page found googling)::
http://www.alpertron.com.ar/ECM.HTM
using 2nd calc "Batch factorization".

If I put 18236498188585393201 and press "Only test primality" button I got:
"18236498188585393201 is prime"

If I use "Factor expressions" button then I got:
"18236498188585393201 = 83 * 2526913 * 86950696619"

WOW!
Bad luck.

--ivica

----- Original Message ----- 
From: "Max Alekseyev" <maxale at gmail.com>
To: "Ivica Kolar" <telpro at kvid.hr>
Cc: <seqfan at ext.jussieu.fr>
Sent: Wednesday, March 19, 2008 2:51 PM
Subject: Re: A110907


> Dear Ivica,
> 
> I do NOT confirm your values. They all turn to be wrong.
> In particular, neither of numerator or denominator of the fraction
> corresponding to n = 40 is prime:
> 
> On Wed, Mar 19, 2008 at 4:41 AM, Ivica Kolar <telpro at kvid.hr> wrote:
>>    40                 18236498188585393201
>>  9118249094292696601
> 
> The prime factorizations of the numerator and denominator are:
> 
> 18236498188585393201 =  83 * 2526913 * 86950696619
> 
> 9118249094292696601 = 33703 * 270547105429567
> 
> Moreover, there are no new terms of A110907 below 1000, besides
> currently listed 1, 2, 6, 12.
> 
> btw, these are the explicit formulas for the numerator and denominator
> of a fraction appearing at the nth step of the recurrent process in
> A110907:
> 
> p(n) = (3^(n+1) + (-1)^(n+1)) / 2
> q(n) = (3^(n+1) - (-1)^(n+1)) / 4
> 
> In particular, they imply the  following necessary condition:
> 
> * if n belongs to A110907 then n+1 is prime.
> 
> as well as a simpler description of A110907 (that I suggest to use
> instead of the current rather complicated one):
> 
> Numbers n such that both (3^(n+1) - 1)/2 and (3^(n+1) + 1)/4 are prime.
> 
> Regards,
> Max
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