A382441 - OEIS

%I #13 Mar 28 2025 08:03:26

%S 1,2,5,7,8,9,10,16,20,32,40,50,51,53,64,83,93,100,117,118,126,160,186,

%T 200,207,224,250,288,311,320,352,372,391,400,448,480,500,625,640,713,

%U 800,960,979,1000,1011,1039,1043,1097,1099,1173,1200,1250,1359,1426

%N 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 This sequence contains all powers of 10.

%H Rémy Sigrist, <a href="/A382441/b382441.txt">Table of n, a(n) for n = 1..1000</a>

%H Rémy Sigrist, <a href="/A382441/a382441.txt">C++ program</a>

%e a(1) = 1.

%e a(2) must not divide 1; we can take a(2) = 2.

%e a(3) must not divide 1, 2 or 12; we can take a(3) = 5.

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o     an, s, d = 1, "1", [1]

%o     while True:

%o         yield an

%o         an = next(k for k in count(an+1) if not any(di%k == 0 for di in d))

%o         for di in str(an):

%o             s += di

%o             d += [si for i in range(len(s)) if (si:=int(s[i:])) > an]

%o         d = sorted(set(d))

%o print(list(islice(agen(), 54))) # _Michael S. Branicky_, Mar 26 2025

%o (C++) // See Links section.

%Y Cf. A048991, A382442 (binary variant), A382445.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Mar 25 2025