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%I #14 Jan 02 2023 12:30:51
%S 1,2,3,4,5,6,8,11,15,25,22,20,24,27,9,12,16,32,33,30,40,18,36,44,37,
%T 45,50,60,48,64,72,54,55,66,73,77,7,14,21,28,42,70,35,75,82,110,41,
%U 108,111,125,132,135,150,225,202,220,200,240,80,120,128,192,216,243,270
%N a(1)=1; a(n+1) is the smallest positive integer not yet used where the digits of the decimal expansion (disregarding all leading and trailing zeros) of a(n)/a(n+1) have no digit in common with either a(n) or a(n+1).
%C Positive powers of ten (A011557) and pandigital numbers (A050289 and A171102) will never appear.
%C Is the sequence finite?
%H Hans Havermann, <a href="/A257664/b257664.txt">Table of n, a(n) for n = 1..2000</a>
%H Eric Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2015-July/015032.html">Division with no visible digits</a>, SeqFan list, July 9, 2015.
%e a(2) is 2 because it is the smallest number not yet used where the digits of a(1)/a(2) = .5, i.e., 5, is neither 1 nor 2.
%e a(3) is 3 because it is the smallest number not yet used where the digits of a(2)/a(3) = .666.., i.e., 6, is neither 2 nor 3.
%e a(4) is 4 because it is the smallest number not yet used where the digits of a(3)/a(4) = .75, i.e., 5 and 7, are neither 3 nor 4.
%e a(72) is 63 because it is the smallest number not yet used where the digits of a(71)/a(72) = 90/63 = 1.42857142857.., i.e., 1, 2, 4, 5, 7, and 8, are not any of 0, 3, 6, or 9.
%e a(376) is 15000 because it is the smallest number not yet used where the digits of a(375)/a(376) = 1025/15000 = .068333.., i.e., 3, 6, and 8 (the zero is leading) are not any of 0, 1, 2, or 5.
%t t = 1; s = {1}; Do[c = 1; d = IntegerDigits[t]; While[Intersection[Flatten[RealDigits[t/c][[1]]], Join[IntegerDigits[c], d]] != {} || MemberQ[s, c], c++]; t = c; AppendTo[s, t], {400}]; s
%K nonn,base
%O 1,2
%A _Eric Angelini_ and _Hans Havermann_, Jul 12 2015
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