[seqfan] Numbers on the string

Eric Angelini Eric.Angelini at kntv.be
Thu Jul 10 14:16:30 CEST 2014


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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