[math-fun] Hits when concatenating?

Hello Math-Fun Say we add the last odd digit of S to a(n): S=1,2,3,6,9,18,19,28,37,44,51,52,57,64,71,72, 79,88,97,104,105,110,111,112,113,116,117,124,... Say we have a hit when the concatenation of two or more initial terms of S reappear in S; will we ever find a hit here (the hit « 123 » was missed by a single unit with « 124 », in the above example; the next possibilities would be with 1236, 12369, 1236918,... but the margin of this post, etc. Best, É.