[seqfan] Quick and fun permutation

[Eric Angelini]

Hello SeqFans,

Start S with a(1) = 1
Extend S with the smallest integer not yet present 
whose leftmost digit divides a(n). I get (by hand, 
in a couple of seconds):

S = 1,10,2,11,12,3,13,14,7,15,5,16,4,17,18,6,19,100,20,21,30,31,101,102,22,23,103,104,8,24,25,50,26,27,9,33,...

Example:
10 is the smallest available integer beginning with '1' 
   -- and this '1' is the only digit dividing a(1)
 2 is the smallest available integer beginning with '2' 
   -- and this '2' divides a(2)
11 is the smallest available integer beginning with '1' 
   -- and this '1' is the only digit dividing a(3)
12 is the smallest available integer beginning with '1' 
   -- and this '1' divides a(4)
 3 is the smallest available integer beginning with '3' 
   -- and this '3' divides a(5)

Every prime in S is followed by an integer starting with '1'.
S is a nice permutation of the integers > 0.

Best,
É.