[seqfan] Re: Numbers on the string

[Neil Sloane]

This is now A244890.

On Thu, Jul 10, 2014 at 11:24 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
>> I believe you missed
>
> ... Ooh, yes indeed, Robert -- many thanks!
> Best,
> É.
>
>
> -----Message d'origine-----
> De : SeqFan [mailto:seqfan-bounces at list.seqfan.eu] De la part de israel at math.ubc.ca
> Envoyé : jeudi 10 juillet 2014 17:12
> À : Sequence Fanatics Discussion list
> Objet : [seqfan] Re: Numbers on the string
>
> I believe you missed
>
> {300, 400, 500, 600, 700, 800, 900, 1100, 1112, 1122, 1132, 1142, 1152, 1162, 1172, 1182, 1192, 2010}
>
> Here's my Maple program:
>
> Stringed:= proc(n)
>  uses GraphTheory;
>  local L,G,E,d;
>  L:= convert(n,base,10);
>  d:= nops(L);
>  E:= select(e -> e[2] <= d and e[2] >= 1,
>    {seq(seq([i,i+s*(1+L[i])],s=[1,-1]),i=1..d)})
>    union {seq([0,i],i=1..d)} union {seq([i,0],i=1..d)};;  G:= Digraph([$0..d],E);  IsHamiltonian(G); end proc;
>
> select(Stringed, {$0..2020});
>
> Cheers,
> Robert
>
> On Jul 10 2014, Eric Angelini wrote:
>
>>
>>Hello SeqFans,
>>We call 2014 a "stringed number" because there is a "string"
>>that links the digits of 2014 in this way:
>>start on 0, jump over 0 digits and land on 1, jump over 1 digit and
>>land on 2, jump over 2 digits and land on 4 -- stop.
>>(Jump to the right or to the left, as you wish, but always remain
>>inside the integer -- 2 and 4, here, are not neighbors).
>>
>>An integer having only one digit is, by definition, a "stringed
>>number".
>>
>>80 is another example of stringed number - but 957 is not, of course,
>>as 1111 is not (we want "single-string" integers, not integers having
>>two or more independent strings -- as in 1111 or 957).
>>
>>Some "stringed numbers" are "stringed-loops" - 1102, for instance,
>>because any digit of 1102 could be a starting or an ending point.
>>
>>How does the "stringed-numbers" sequence look like (I couldn't find it
>>in the OEIS, if I'm not wrong)?
>>
>> S =
>> 0,1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100,101,102,103,104,105,106,107,108,109,110,120,130,140,150,160,170,180,190,200,201,301,401,501,601,701,801,901,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1011,1021,1031,1041,1051,1061,1071,1081,1091,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1201,1202,1301,1302,1401,1402,1501,1502,1601,1602,1701,1702,1801,1802,1901,1902,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,...
>>
>>Are there more "stringed-loops" integers than 1102 and 2011?
>>
>>What is the smallest integer showing the 10 digits at least once
>>- is it 8642013579?
>>Best,
>>É.
>>
>>
>>
>>
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>>
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>>
>>
>
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-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com