[seqfan] A vertical stroke between all consecutive 1's

Eric Angelini Eric.Angelini at kntv.be
Thu Mar 10 18:55:33 CET 2011


Hello SeqFans,

A = 1,10,3,4,5,6,7,8,9,11,21,12,31,13,14,110,15,41,16,17,18,112,19,20,51,100,101,201,102,22,23,24,211,...

Now insert a vertical stroke between all consecutive 1's:

A = 1,10,3,4,5,6,7,8,9,1 1,21,12,31,13,14,1 10,15,41,16,17,18,112, 19,20,51,100,101,201,102,22,23,24,211,...
A = 1|10,3,4,5,6,7,8,9,1|1,21|12,31|13,14,1|10,15,41|16,17,18,1|12,19,20,51|100,101,201|102,22,23,24,21|1,...

The quantity of digits between two strokes is given by A itself:

A = 1|10,3,4,5,6,7,8,9,1|1,21|12,31|13,14,1|10,15,41|16,17,18,1|12,19,20,51|100,101,201|102,22,23,24,21|1,...
    1          10          3    4      5        6         7          8           9             11

A is the lexicographically first such sequence; to build it we always use the smallest available integer not yet present in A and not leading to a contradiction.

Could someone be so kind to computer a hundred terms or so?

The same procedure is used here for consecutive 2's, 3's, etc.
http://www.cetteadressecomportecinquantesignes.com/Runs2.htm

Best,
É.




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