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 A333594 Lexicographically earliest sequence of distinct positive integers such that the decimal expansion 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), with a(1) = 7. 1

%I

%S 7,14,42,28,84,77,9,18,5,3,2,6,8,4,11,40,12,400,22,24,72,44,36,16,48,

%T 30,20,60,33,37,45,15,50,150,54,66,55,82,75,25,220,32,288,96,396,88,

%U 64,192,576,640,480,80,160,360,63,70,21,700,140,420,126,4158,154,462,1540,518,1188,444,74,90,27,81,165,495,297,99

%N Lexicographically earliest sequence of distinct positive integers such that the decimal expansion 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), with a(1) = 7.

%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?

%H Carole Dubois, <a href="/A333594/b333594.txt">Table of n, a(n) for n = 1..300</a>

%e a(1)/a(2) = 7/14 = .5 and a(2)/a(1) = 14/7 = 2 and their combined distinct significant digits (2,5) are exclusive of the combined distinct digits of a(1) and a(2), (1,4,7).

%e a(5)/a(6) = 84/77 = 1.090909... and a(6)/a(5) = 77/84 = .916666... and their combined distinct significant digits (0,1,6,9) are exclusive of the combined distinct digits of a(5) and a(6), (4,7,8).

%e a(299)/a(300) = 656/21648 = .03030303... and a(300)/a(299) = 21648/656 = 33 and their combined distinct significant digits (0,3) is exclusive of the combined distinct digits of a(299) and a(300), (1,2,4,5,6,8).

%Y Cf. A333480 (where a(1) = 2).

%K base,nonn

%O 1,1

%A _Carole Dubois_ and _Eric Angelini_, Mar 27 2020

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Last modified January 27 05:36 EST 2021. Contains 340455 sequences. (Running on oeis4.)