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Lexicographically earliest sequence of distinct positive integers such that the decimal expansions of neither a(n)/a(n+1) nor a(n+1)/a(n) contains a significant digit present in either a(n) or a(n+1).
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%I #8 Jan 09 2021 02:08:20

%S 2,3,5,6,8,4,11,40,12,400,22,24,72,44,36,9,18,48,16,80,33,37,45,15,50,

%T 30,20,60,54,66,55,82,75,25,220,32,288,96,396,88,64,192,576,640,480,

%U 144,4000,110,41,148,74,90,27,81,165,495,297,99,198,540,150,444,364,2002,224,42,7,14,70,21

%N Lexicographically earliest sequence of distinct positive integers such that the decimal expansions of neither a(n)/a(n+1) nor a(n+1)/a(n) contains a significant digit present in either a(n) or a(n+1).

%C By "significant digit" we mean to exclude from the quotients any zeros preceding the first nonzero digit, as well as zeros following the last nonzero digit (as in a terminating decimal).

%C Is the sequence infinite?

%e a(1)/a(2) = 2/3 = 0.666... and a(2)/a(1) = 3/2 = 1.5 and their combined distinct significant digits (1,5,6) are exclusive of the combined distinct digits of a(1) and a(2), (2,3).

%e a(7)/a(8) = 11/40 = 0.275 and a(8)/a(7) = 40/11 = 3.636363... and their combined distinct significant digits (2,3,5,6,7) are exclusive of the combined distinct digits of a(7) and a(8), (0,1,4).

%e a(106)/a(107) = 624/208 = 3 and a(107)/a(106) = 208/624 = 0.333... and their combined distinct significant digits (3) is exclusive of the combined distinct digits of a(106) and a(107), (0,2,4,6,8).

%K nonn,base

%O 1,1

%A _Eric Angelini_ and _Hans Havermann_, Mar 23 2020