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A347180 Lexicographically earliest sequence of distinct positive integers such that the first digit of a(n) is visible in a(n) * a(n+1).

%I A347180 #16 Aug 24 2021 14:34:50
%S A347180 1,10,11,12,9,21,2,6,16,7,25,5,3,13,8,23,4,26,17,30,31,14,15,34,39,24,
%T A347180 18,45,32,41,28,19,22,33,40,35,38,36,37,29,42,20,46,27,47,52,49,50,43,
%U A347180 48,51,54,64,44,55,53,65,56,63,58,61,60,66,57,62,59,67,68,69,72,76,75,73,79,82,71,70
%N A347180 Lexicographically earliest sequence of distinct positive integers such that the first digit of a(n) is visible in a(n) * a(n+1).
%e A347180 a(1) * a(2) =  1 * 10 =  10;
%e A347180 a(2) * a(3) = 10 * 11 = 110;
%e A347180 a(3) * a(4) = 11 * 12 = 132;
%e A347180 a(4) * a(5) = 12 *  9 = 108;
%e A347180 a(5) * a(6) =  9 * 21 = 189; etc.
%o A347180 (Python)
%o A347180 def aupton(terms):
%o A347180     alst, aset = [1], {1}
%o A347180     while len(alst) < terms:
%o A347180         an, target = 2, str(alst[-1])[0]
%o A347180         while an in aset or target not in str(alst[-1]*an): an += 1
%o A347180         alst.append(an); aset.add(an)
%o A347180     return alst
%o A347180 print(aupton(200)) # _Michael S. Branicky_, Aug 21 2021
%Y A347180 Cf. A333774, A347181.
%K A347180 base,nonn
%O A347180 1,2
%A A347180 _Eric Angelini_ and _Carole Dubois_, Aug 21 2021