[seqfan] Re: Scott Shannon's "Grow" sequence A332580 (and A332584)

Neil Sloane njasloane at gmail.com
Thu Feb 20 16:49:11 CET 2020

Sean,  I think Scott had searched for a(44) out to about 4 million.

Joseph, Your a(98) = 259110640 is a number with 2220884473 digits (unless I
miscounted!), very impressive.

For a(44), suppose we just tried to prove that it exists, without looking
for the smallest solution.

Joseph, obviously you aren't doing a brute force search.  Could your
method of attack be modified as follows: suppose there is a solution, not
minimal, just a solution,
with say 14 digits. Let G = the Giant Prefix cat(44,45,...,10^13-1), then
set up the obvious recurrence
T_{i+1} = 10^14 * T_i + i, starting with T_0 = G. We want a T_i that is
divisible by 10^13+i+1, so to study that
we work over the ring Z/(10^13+i+1) Z - and reduce everything in sight mod
that number.

I'm sure I'm not telling you anything you aren't already using.  All I'm
really saying is that it might be easier to look for a single solution, a
long way out, rather than the minimal solution.

On Thu, Feb 20, 2020 at 8:42 AM Neil Sloane <njasloane at gmail.com> wrote:

> That is fabulous!  So a(98) exists!!   I have regained my belief that they
> all exist. Probability rules!
> On Wed, Feb 19, 2020 at 11:16 PM Joseph Myers <jsm at polyomino.org.uk>
> wrote:
>> On Thu, 20 Feb 2020, Sean A. Irvine wrote:
>> > I'm not sure how far Scott already searched but I have a(92) > 3000000
>> and
>> > a(98) > 3500000. (I haven't tried 44).
>> I get a(98) = 259110640, a(44) > 10^10 and a(92) > 3.6*10^9.
>> --
>> Joseph S. Myers
>> jsm at polyomino.org.uk
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/

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