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Lexicographically earliest sequence of distinct positive integers such that the first digit of a(n) is visible in a(n) * a(n+1).
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%I #16 Aug 24 2021 14:34:50

%S 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 18,45,32,41,28,19,22,33,40,35,38,36,37,29,42,20,46,27,47,52,49,50,43,

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

%e a(1) * a(2) = 1 * 10 = 10;

%e a(2) * a(3) = 10 * 11 = 110;

%e a(3) * a(4) = 11 * 12 = 132;

%e a(4) * a(5) = 12 * 9 = 108;

%e a(5) * a(6) = 9 * 21 = 189; etc.

%o (Python)

%o def aupton(terms):

%o alst, aset = [1], {1}

%o while len(alst) < terms:

%o an, target = 2, str(alst[-1])[0]

%o while an in aset or target not in str(alst[-1]*an): an += 1

%o alst.append(an); aset.add(an)

%o return alst

%o print(aupton(200)) # _Michael S. Branicky_, Aug 21 2021

%Y Cf. A333774, A347181.

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Carole Dubois_, Aug 21 2021