[seqfan] Re: Numbers on the string

[israel at math.ubc.ca]

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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