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A382445 Lexicographically least increasing sequence of distinct positive integers such that for any n > 1, a(n) does not divide the concatenation of the earlier terms.

%I A382445 #8 Mar 28 2025 08:03:17
%S A382445 1,2,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
%T A382445 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,
%U A382445 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70
%N A382445 Lexicographically least increasing sequence of distinct positive integers such that for any n > 1, a(n) does not divide the concatenation of the earlier terms.
%H A382445 Rémy Sigrist, <a href="/A382445/a382445.gp.txt">PARI program</a>
%e A382445 a(1) = 1.
%e A382445 a(2) must not divide 1; we can take a(2) = 2.
%e A382445 a(3) must not divide 12; we can take a(3) = 5.
%o A382445 (Python)
%o A382445 from itertools import count, islice
%o A382445 def agen(): # generator of terms
%o A382445     an = t = 1
%o A382445     while True:
%o A382445         yield an
%o A382445         an = next(k for k in count(an+1) if t%k != 0)
%o A382445         t = t*10**len(str(an)) + an
%o A382445 print(list(islice(agen(), 54))) # _Michael S. Branicky_, Mar 26 2025
%o A382445 (PARI) \\ See Links section.
%Y A382445 Cf. A007978, A096098, A382441.
%K A382445 nonn,base
%O A382445 1,2
%A A382445 _Rémy Sigrist_, Mar 25 2025