[seqfan] Divisors of the concatenation of n and n+1

[Eric Angelini]

Hello SeqFans,
a(n) is the smallest unused integer so far in S such that a(n) is a divisor of the concatenation of n and n+1.

     n =  1  2  3  4  5  6  7  8  9   10   11   12   13   14   15   16   17   18   19   20   21   22 
concat = 12 23 34 45 56 67 78 89 910 1011 1112 1213 1314 1415 1516 1617 1718 1819 1920 2021 2122 2223 
     S =  1,23, 2, 3, 4,67, 6,89, 5,  337,  8, 1213,  9,  283, 379,  7,  859, 17,  10,  43,  13,  14,...

Example:
The divisors of 1314 (concatenation of 13 and 14) are 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657 and 1314.
As 1, 2, 3 and 6 appear already in S, we have a(13) = 9.

Is S a permutation of the integer > 0 ?

Best,
É.