Weak Skolem-Langford integers

[Eric Angelini]

Hello Math-Fun & SeqFans,

Could someone please compute for me all "weak Skolem-Langford" integers ?

The sequence is finite (and ends, I guess, with 978416154798652002).

http://www.research.att.com/~njas/sequences/A108116

Please find hereunder what I have found for integers of length 4, 6 and 8.

Length 4:
2002 

Length 6:
131003, 231213, 300131, 312132,420024 

Length 8:

12132003, 14130043, 15120025, 23121300, 23421314, 25121005, 25320035, 30023121, 31213200, 31413004, 34003141, 40031413, 41312432, 45001415, 45121425, 45300435, 50012152, 51410054, 52002151, 52412154, 53002352, 53400354, 61310036, 62312136, 63001316, 63121326, 64200246.

Lengths 10 to 18?

Best,
Éric A.