# [seqfan] Re: Skolem + digits + loop

M. F. Hasler oeis at hasler.fr
Fri Nov 1 16:42:40 CET 2013

```I propose this as https://oeis.org/draft/A227859

As I write in the comment, this could be done for other ranges instead
of {0,...,9}.
Unless I'm wrong, {0,1} and {0,1,2} are not possible,
but {0,2} could be possible, viz
0,0,2,0,0,2,*0,0,2,0,0,2,...
or
0,0,2,0,0,2,*2,0,0,2,...
At the point *, two choices are possible, I think the second one is the better
(since we "used up" already the second pair 0,0, it should be the turn
of the second pair 2,2)
but the first yields a lexicographically smaller sequence having as
many 2's than 0's (though they have only half the density).
The range {0,1,2,3} would correspond to
0,0,1,2,1,3,2,0,0,3,1,2,1,3,2,0,0,3,1,2,1,...

Maximilian

On Fri, Nov 1, 2013 at 5:43 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Sorry, folks, the loop was there, under
> my very eyes... Always drink an espresso
> before sending, I know...
>
> Propulsé d'un aPhone
>
>
>
> Le 1 nov. 2013 à 10:40, "Eric Angelini" <Eric.Angelini at kntv.be> a écrit :
>
>>
>> Hello SeqFans,
>> can't find this seq K in the OEIS...
>> K=0,0,1,2,1,3,2,4,5,3,6,7,4,8,5,9,1,6,1,7,0,0,8,2,3,9,2,4,3,5,6,7,4,8,9,5,1,6,1,7,0,0,8,2,9,3,2,4,5,3,6,7,4,8,5,9,1,6,1,7,0,0,8,2,3,9,2,4,3,5,6,7,4,8,9,5,1,6,1,7,0,0,8,2,9,3,2,...
>>
>> Rules:
>> - all integers of K are >= 0 and <= 9
>> - there are d integers between each pair of successive d integers
>> - K was extended trying always to insert the smallest pair of integers not
>> yet inserted in K
>> - when the first 9-9 pair of integers has
>> been inserted, start a new cycle with
>> the second set of pairs (0-0,1-1,2-2,...
>> 9-9)
>> - Never start a new cycle before the
>> previous one has been completed.
>>
>> Question:
>> At some point K has to enter into a loop,
>> I guess. But when and which loop?
>>
>> Best,
>> É.
>>
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
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>
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```