[seqfan] Fun and quick permutation (with a digital root)

[Eric Angelini]

Hello SeqFans (last posting of the day, my apologizes)

Here is another simple permutation of the integers > 0.
Start S with a(1) = 1
Extend S with the smallest unused integer so far such 
that a(n+1) starts with the digital root of a(n). I get:

S = 1,10,11,2,20,21,3,30,31,4,40,41,5,50,51,6,60,61,7,70,71,8,80,81,9,90,91,12,32,52,72,92,22,42,62,82,13,43,73,17,53,83,23,...

Example:
10 is the smallest available integer with '1' as leftmost digit 
   -- this '1' being the digital root of a(1);
11 is the smallest available integer with '1' as leftmost digit 
   -- this '1' being the digital root of a(2);
 2 is the smallest available integer with '2' as leftmost digit 
   -- this '2' being the digital root of a(3);
20 is the smallest available integer with '2' as leftmost digit 
   -- this '2' being the digital root of a(4);
...
[look now at the present end of S]:
...
23 is the smallest available integer with '2' as leftmost digit 
   -- this '2' being the digital root of the term coming before 23
   (the digital root of 83 is 8+3=11 then 1+1=2)

Best,
É.