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A361339 a(n) is the smallest k such that A361338(k) = n.

%I A361339 #24 Apr 05 2023 22:23:01
%S A361339 1,112,139,219,373,719,1133,1919,3377,17117
%N A361339 a(n) is the smallest k such that A361338(k) = n.
%e A361339      a(n) n  {the digits reached}
%e A361339        1  1  {1}
%e A361339      112  2  {2, 4}
%e A361339      139  3  {8, 4, 7}
%e A361339      219  4  {8, 2, 4, 6}
%e A361339      373  5  {1, 2, 4, 6, 8}
%e A361339      719  6  {0, 2, 4, 6, 8, 9}
%e A361339     1133  7  {0, 2, 4, 6, 7, 8, 9}
%e A361339     1919  8  {0, 2, 4, 5, 6, 7, 8, 9}
%e A361339     3377  9  {0, 2, 3, 4, 5, 6, 7, 8, 9}
%e A361339    17117 10  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
%t A361339 With[{s = Import["https://oeis.org/A361338/b361338.txt", "Data"][[All, -1]]}, {1}~Join~Table[-1 + FirstPosition[s, k][[1]], {k, 2, 10}]] (* _Michael De Vlieger_, Apr 04 2023, using bfile at A361338 *)
%o A361339 (Python)
%o A361339 from itertools import count
%o A361339 def agen():
%o A361339     n, adict = 1, dict()
%o A361339     for k in count(1):
%o A361339         v = A361338(k) # uses A361338() and reach1() in A361338
%o A361339         if v not in adict: adict[v] = k
%o A361339         while n in adict: yield adict[n]; n += 1
%o A361339         if n == 11: return
%o A361339 print(list(agen())) # _Michael S. Branicky_, Apr 04 2023
%Y A361339 Cf. A361337-A361349.
%K A361339 nonn,base,fini,full
%O A361339 1,2
%A A361339 _N. J. A. Sloane_, Apr 04 2023, based on an email from _Michael S. Branicky_