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A382441 Lexicographically earliest sequence of positive integers such that for any n > 1, a(n) does not divide any of the positive numbers whose decimal expansion appears as a contiguous subword in the concatenation of the previous terms.

%I A382441 #13 Mar 28 2025 08:03:26
%S A382441 1,2,5,7,8,9,10,16,20,32,40,50,51,53,64,83,93,100,117,118,126,160,186,
%T A382441 200,207,224,250,288,311,320,352,372,391,400,448,480,500,625,640,713,
%U A382441 800,960,979,1000,1011,1039,1043,1097,1099,1173,1200,1250,1359,1426
%N A382441 Lexicographically earliest sequence of positive integers such that for any n > 1, a(n) does not divide any of the positive numbers whose decimal expansion appears as a contiguous subword in the concatenation of the previous terms.
%C A382441 This sequence contains all powers of 10.
%H A382441 Rémy Sigrist, <a href="/A382441/b382441.txt">Table of n, a(n) for n = 1..1000</a>
%H A382441 Rémy Sigrist, <a href="/A382441/a382441.txt">C++ program</a>
%e A382441 a(1) = 1.
%e A382441 a(2) must not divide 1; we can take a(2) = 2.
%e A382441 a(3) must not divide 1, 2 or 12; we can take a(3) = 5.
%o A382441 (Python)
%o A382441 from itertools import count, islice
%o A382441 def agen(): # generator of terms
%o A382441     an, s, d = 1, "1", [1]
%o A382441     while True:
%o A382441         yield an
%o A382441         an = next(k for k in count(an+1) if not any(di%k == 0 for di in d))
%o A382441         for di in str(an):
%o A382441             s += di
%o A382441             d += [si for i in range(len(s)) if (si:=int(s[i:])) > an]
%o A382441         d = sorted(set(d))
%o A382441 print(list(islice(agen(), 54))) # _Michael S. Branicky_, Mar 26 2025
%o A382441 (C++) // See Links section.
%Y A382441 Cf. A048991, A382442 (binary variant), A382445.
%K A382441 nonn,base
%O A382441 1,2
%A A382441 _Rémy Sigrist_, Mar 25 2025