A110907

[Max Alekseyev]

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