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A351820 a(1) = 1, a(2) = 2, a(3) = 3 and a(n) is the smallest number not included earlier that divides the concatenation a(n-3), a(n-2), a(n-1).

%I A351820 #21 Feb 22 2022 03:40:52
%S A351820 1,2,3,41,2341,9,1374473,7,123,13,49,53,91,689,5391689,167,8429,17,11,
%T A351820 21,211,37,89,2113789,47,89211378947,1336372981,43,169,7213,47966357,
%U A351820 121,13681,29863,9848521381,173,23,2997821,29,39,19,97973,130665991,727,251,817
%N A351820 a(1) = 1, a(2) = 2, a(3) = 3 and a(n) is the smallest number not included earlier that divides the concatenation a(n-3), a(n-2), a(n-1).
%H A351820 Jon E. Schoenfield, <a href="/A351820/b351820.txt">Table of n, a(n) for n = 1..5000</a>
%e A351820 a(4) = 41 is the smallest unused integer that divides 123;
%e A351820 a(5) = 2341 is the smallest unused integer that divides 2341;
%e A351820 a(6) = 9 is the smallest unused integer that divides 3412341;
%e A351820 a(7) = 1374473 is the smallest unused integer that divides 4123419; etc.
%t A351820 nn = 46; s = Range[3]; c[_] = 0; Array[Set[{a[#1], c[#2]}, {#2, #1}] & @@ {#, s[[#1]]} &, Length[s]]; Do[(Set[{a[n], c[#]}, {#, n}] &@ SelectFirst[Divisors[FromDigits@ Flatten@ Map[IntegerDigits, Reverse@ Array[a[n - #] &, 3]]], c[#] == 0 &]), {n, 1 + Length[s], nn}]; Array[a[#] &, nn] (* _Michael De Vlieger_, Feb 20 2022 *)
%o A351820 (Python)
%o A351820 from sympy import divisors
%o A351820 def aupton(terms):
%o A351820     alst, aset = [1, 2, 3], {1, 2, 3}
%o A351820     while len(alst) < terms:
%o A351820         concat = int("".join(map(str, alst[-3:])))
%o A351820         an = min(d for d in divisors(concat) if d not in aset)
%o A351820         alst.append(an); aset.add(an)
%o A351820     return alst
%o A351820 print(aupton(46)) # _Michael S. Branicky_, Feb 20 2022
%Y A351820 Cf. A085946, A351629.
%K A351820 base,nonn
%O A351820 1,2
%A A351820 _Carole Dubois_ and _Eric Angelini_, Feb 20 2022
%E A351820 a(26) and beyond from _Michael S. Branicky_, Feb 20 2022