%I #21 Mar 11 2021 20:36:42
%S 1,10,12,2,20,22,24,4,14,16,6,26,28,8,18,15,5,25,35,30,3,33,36,32,34,
%T 38,48,40,42,21,27,57,45,50,52,54,44,46,56,58,68,60,62,64,66,63,39,9,
%U 69,90,70,7,77,147,49,84,74,37,333,93,31,124,72,75,51,17,102,80,78,76,86,82,88,98,91
%N a(1) = 1, a(2) = 10; for n > 2, a(n) is the least positive integer not occurring earlier that shares both a factor and a digit with a(n-1).
%C After 100000 terms the lowest unused number is 18181. The sequence is likely a permutation of the positive integers.
%H Scott R. Shannon, <a href="/A342356/a342356.png">Image of the first 100000 terms</a>. The green line is a(n) = n.
%t Block[{a = {1, 10}, m = {1, 0}, 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, 73}]; a] (* _Michael De Vlieger_, Mar 11 2021 *)
%o (Python)
%o from sympy import factorint
%o def aupton(terms):
%o alst, aset = [1, 10], {1, 10}
%o for n in range(3, terms+1):
%o an = 1
%o anm1_digs, anm1_factors = set(str(alst[-1])), set(factorint(alst[-1]))
%o while True:
%o while an in aset: an += 1
%o if set(str(an)) & anm1_digs != set():
%o if set(factorint(an)) & anm1_factors != set():
%o alst.append(an); aset.add(an); break
%o an += 1
%o return alst
%o print(aupton(75)) # _Michael S. Branicky_, Mar 09 2021
%Y Cf. A342366 (share factor but not digit), A239664 (no shared factor or digit), A342367 (share digit but not factor), A184992, A309151, A249591.
%K nonn,base
%O 1,2
%A _Scott R. Shannon_, Mar 08 2021