[seqfan] Re: More terms for A195265 and A230305 ?

[Hans Havermann]

On Oct 27, 2013, at 2:56 AM, Neil Sloane <njasloane at gmail.com> wrote:

> Dear Seqfans, A195265 was created in 2011, but presumably we have better
> factoring algorithms now and more computers and
> more people and a bigger cloud.

The table that I submitted for http://oeis.org/A195264 (see 'links' therein) is still actively maintained by me. That includes all unknown-outcome evolutions starting with numbers up to 10000. If you click in that table on the 'unknown' beside the number 20 it will give you the current state of the evolution. There was a bit of a bottleneck at Alonso20(102) [= A195265(103); we're using offset zero for our evolutions] involving a 62-digit factor, cracked by a Mathew in MersenneForum on August 13. Sean A. Irvine subsequently extended that to Alonso20(109). The unfactored composite in Alonso20(110) is 178 digits long. I maintain links to sorted lists of unfactored composites at the *bottom* of the aforementioned table (here, http://chesswanks.com/seq/a195264/ ). If anyone can factor any of these composites, submit the factorization to factordb.com and I will (eventually) find it; a personal heads-up would of course be appreciated. I'll see what I can do about the b-file.