definition of anti-divisor

[Max Alekseyev]

On 7/23/07, Max Alekseyev <maxale at gmail.com> wrote:

> Therefore, every element of A066466, except 4, must be of the form
> 3*2^k such that 3*2^(k+1)-1, 3*2^(k+1)+1 are twin primes. There no
> such new k (i.e., except known 1,2,6,18) below 1000.

Small corrections: 1,2,6,18 above correspond to k+1 not k.
In other words, 3*2^n - 1, 3*2^n + 1 are twin primes for n=1,2,6,18.

According to these tables:
http://www.prothsearch.net/riesel.html
http://www.prothsearch.net/riesel2.html
there are no other such n up to 1200000.
Therefore, the next element of A066466 (if it exists) is greater than
3*2^1200000 ~= 10^361236.

Max