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A342367 a(1) = 1; for n > 1, a(n) is the least positive integer not occurring earlier that shares a digit but not a factor > 1 with a(n-1).

%I A342367 #11 Mar 11 2021 20:38:07
%S A342367 1,10,11,12,13,3,23,2,21,16,15,14,17,7,27,20,29,9,19,18,31,30,37,32,
%T A342367 25,22,123,26,61,6,65,36,35,33,34,39,38,43,4,41,24,47,40,49,44,45,46,
%U A342367 63,53,5,51,50,57,52,55,54,59,56,67,60,101,70,71,72,73,74,75,58,81,8,83,28,85,48
%N A342367 a(1) = 1; for n > 1, a(n) is the least positive integer not occurring earlier that shares a digit but not a factor > 1 with a(n-1).
%C A342367 After 100000 terms the lowest unused number is 99986. It is almost certain that this sequence is a permutation of the positive integers.
%H A342367 Scott R. Shannon, <a href="/A342367/a342367.png">Image of the first 1000 terms</a>. The green line is a(n) = n.
%t A342367 Block[{a = {1}, m = {1}, k}, Do[k = 2; While[Nand[FreeQ[a, k], GCD[k, a[[-1]]] == 1, IntersectingQ[m, IntegerDigits[k]]], k++]; AppendTo[a, k]; Set[m, IntegerDigits[k]], {i, 74}]; a] (* _Michael De Vlieger_, Mar 11 2021 *)
%o A342367 (Python)
%o A342367 from sympy import factorint
%o A342367 def aupton(terms):
%o A342367   alst, aset = [1], {1}
%o A342367   for n in range(2, terms+1):
%o A342367     an = 1
%o A342367     anm1_digs, anm1_factors = set(str(alst[-1])), set(factorint(alst[-1]))
%o A342367     while True:
%o A342367       while an in aset: an += 1
%o A342367       if set(str(an)) & anm1_digs != set():
%o A342367         if set(factorint(an)) & anm1_factors == set():
%o A342367           alst.append(an); aset.add(an); break
%o A342367       an += 1
%o A342367   return alst
%o A342367 print(aupton(74)) # _Michael S. Branicky_, Mar 09 2021
%Y A342367 Cf. A342356 (share factor and digit), A342366 (share factor but not digit), A239664 (no shared factor or digit), A184992, A309151, A249591.
%K A342367 nonn,base
%O A342367 1,2
%A A342367 _Scott R. Shannon_, Mar 09 2021