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A347182 Lexicographically earliest sequence of distinct positive integers such that all digits of a(n) are visible in a(n) * a(n+1).

%I A347182 #25 Aug 24 2021 17:57:55
%S A347182 1,10,11,91,9,21,6,16,26,24,18,45,12,51,3,13,27,36,38,22,56,28,29,32,
%T A347182 41,4,31,23,14,76,89,55,47,42,7,25,5,15,34,69,39,61,92,86,8,35,67,100,
%U A347182 17,43,78,87,33,71,81,64,54,66,96,72,99,101,109,90,44,102,60,46,79,48,58,98,151,75,37,19
%N A347182 Lexicographically earliest sequence of distinct positive integers such that all digits of a(n) are visible in a(n) * a(n+1).
%C A347182 a(3) = 11 has two digits "1"; they must both be visible in a(3) * a(4) and this is the case as a(3) * a(4) = 11 * 91 = 1001.
%C A347182 Is this a permutation of the positive integers? - _Pontus von Brömssen_, Aug 23 2021
%H A347182 Pontus von Brömssen, <a href="/A347182/b347182.txt">Table of n, a(n) for n = 1..10000</a>
%e A347182 a(1) * a(2) =  1 * 10 =   10;
%e A347182 a(2) * a(3) = 10 * 11 =  110;
%e A347182 a(3) * a(4) = 11 * 91 = 1001;
%e A347182 a(4) * a(5) = 91 *  9 =  819;
%e A347182 a(5) * a(6) =  9 * 21 =  189; etc.
%o A347182 (Python)
%o A347182 from collections import Counter
%o A347182 def A347182_list(n):
%o A347182     a = [1]
%o A347182     m = 2  # Smallest number not yet in a.
%o A347182     M = 1  # Largest number in a so far.
%o A347182     used = []  # Indicator for what numbers m..M that are in a so far.
%o A347182     for i in range(n - 1):
%o A347182         c0 = Counter(str(a[-1]))
%o A347182         x = m
%o A347182         while 1:
%o A347182             if x > M or not used[x - m]:
%o A347182                 c = Counter(str(a[-1] * x))
%o A347182                 if all(c[d] >= c0[d] for d in "0123456789"):
%o A347182                     break
%o A347182             x += 1
%o A347182         if x > M:
%o A347182             used.extend([0] * (x - M - 1) + [1])
%o A347182             M = x
%o A347182         else:
%o A347182             used[x - m] = 1
%o A347182         if x == m:
%o A347182             j = next((j for j in range(len(used)) if not used[j]), len(used))
%o A347182             m += j
%o A347182             del used[:j]
%o A347182         a.append(x)
%o A347182     return a  # _Pontus von Brömssen_, Aug 24 2021
%Y A347182 Cf. A347180, A347181, A347183.
%K A347182 base,nonn
%O A347182 1,2
%A A347182 _Eric Angelini_ and _Carole Dubois_, Aug 22 2021