[seqfan] Re: Add the biggest absent digit

[Frank Adams-Watters]

(These were done by hand.)

Base 2
1 constant

Base 3
1, 10, 12 constant
Decimal
1, 3, 5

Base 4
1, 10, 13, 21, 30, 32, 33, 101, 103, 111, 120, 123 constant
Decimal
1, 4, 7, 9, 12, 14, 15, 17, 19,  21,  24, 27

Base 5
1, 10, 14, 22, 31, 40, 43, 100, 104, 112, 121, 130, 134, 141, 144, 201, 210, 214, 222, 231, 240, 244, 302, 311, 320, 324, 330, 334, 341, 343, 400, 403, 410, 413, 420, 423, 424, 432, 433, 440, 443, 1000, 1004, 1012, 1021, 1030, 1034, 1041, 1044, 1102, 1111, 1120, 1124, 1132, 1141, 1144, 1202, 1211, 1220, 1224, 1232, 1241, 1300, 1304, 1311, 1320, 1324 constant
Decimal
1, 5, 9, 12, 16, 20, 23, 25, 29, 32, 36, 40, 44, 46, 49, 51, 55, 59, 62, 66, 70, 74, 77, 81, 85, 89, 90, 94, 96, 98, 100, 103, 105, 108, 110, 113, 114, 117, 118, 120, 123, 125, 129, 132, 136, 140, 144, 146, 149, 152, 156, 160, 164, 167, 171, 174, 177, 181, 185, 189, 192, 196, 200, 204, 206, 210, 214

It seems very likely that the sequence for any base always "ends" with a constant. I don't see any way to prove that it will not instead terminate with no possible continuation; for that to happen, it would have to get through all the (k-1) digit numbers in base k without getting a permutation of 1..(k-1).

Franklin T. Adams-Watters

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Tue, Jul 21, 2015 8:33 pm
Subject: [seqfan] Re: Add the biggest absent digit



> becomes constant

... Neat remark, Maximilian!

(Your a(16173532) =
123456798
has been confirmed in a private mail
to me by another list
member.)

Thanks for the submission.
Best,
É.


> Le 22 juil. 2015 à
02:57, M. F. Hasler <seqfan at hasler.fr> a écrit :
> 
> Hello Eric,
> I don't
know whether one can speak of a last term, but the sequence
> becomes constant
from a(16173532) = 123456798 on
> (cf. http://oeis.org/draft/A260263).
> 
>
Maximilian
> 
>> On Tue, Jul 21, 2015 at 10:30 AM, Eric Angelini
<Eric.Angelini at kntv.be> wrote:
>> 
>> Hello SeqFans,
>> What is the last term
of this seq?
>> 
>> -->Start with a(1)=1 and always
>> add to a(n) the
biggest digit not
>> present in a(n).
>> 
>>
-->A=1,10,19,27,36,45,54,63,72,81,
>> 90,98,105,...
>> 
>> Example:
>> The
biggest digit not present in 98 is 7;
>> 98+7=105.
>> 
>> Best,
>> É.
>>
Catapulté de mon aPhone
> 
>
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