# [seqfan] Re: nice new board game puzzle A337663

Peter Kagey peterkagey at gmail.com
Thu Oct 8 21:41:32 CEST 2020

```It looks like Arnauld removed his post for some reason. However, there is a new program that was posted that computes a(5) = 49: https://codegolf.stackexchange.com/a/212182/53884 <https://codegolf.stackexchange.com/a/212182/53884>

pk

> On Oct 8, 2020, at 10:18 AM, Neil Sloane <njasloane at gmail.com> wrote:
>
> I just finished updating A337663 with all the new results.  We still don't
> know a(5)!
>
> On Thu, Oct 8, 2020 at 7:04 AM <hv at crypt.org> wrote:
>
>> Peter Kagey <peterkagey at gmail.com> wrote:
>> :I posted this question to Code Golf Stack Exchange, and Arnauld Chevallier
>> :confirmed the given terms:
>> https://codegolf.stackexchange.com/a/212164/53884
>>
>> I don't see Arnauld's response there, do I need to do something special
>> to see it?
>>
>> :My suspicion is that it will be hard to get more many terms because of
>> :how quickly the search space grows.
>> :
>> :This is a really lovely sequence. I'd be interested to know more about
>> this,
>> :such as:
>> :What is the 'widest' such a game can get? (The above example uses 13
>> columns.)
>>
>> This gets quite tricky: for n >= 5 we can have multiple independent
>> starting
>> clusters, and it is not obvious to me how far away from each other those
>> can be.
>>
>> Starting clusters can be independent only if they are the seed for the
>> placement of one of the numbers 2 to 8, so there can be no more than 7
>> of them. But that independence will make it a whole lot more difficult
>> to calculate for n >= 5.
>>
>> My inclination is to keep them independent, and at each step consider
>> each possible way of placing two or more of them in relation to each
>> other (consistent with prior information) that might generate another
>> possible location for the next integer to be placed. (Taking care,
>> therefore, that no existing entry > 1 acquires a new neighbour. But
>> two 1s _can_ become neighbours.)
>>
>> That sounds quite tough to code, and even tougher to make fast.
>>
>> Hugo
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/

```