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Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, the first nonzero digit of a(n+1)/a(n) is "6".
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%I #8 Oct 29 2019 06:36:42

%S 1,6,4,24,15,9,54,33,2,12,8,5,3,18,11,7,42,26,16,10,60,36,22,14,84,51,

%T 31,19,13,78,47,29,20,120,72,44,27,17,102,62,38,23,138,83,50,30,180,

%U 108,65,39,25,150,90,55,34,21,126,76,46,28,168,101,61,37,222

%N Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, the first nonzero digit of a(n+1)/a(n) is "6".

%C In other words, for any n > 0, we have an integer k such that floor(10^k * a(n+1)/a(n)) = 6.

%H Rémy Sigrist, <a href="/A328757/b328757.txt">Table of n, a(n) for n = 1..10000</a>

%e The first terms, alongside a(n+1)/a(n), are:

%e n a(n) a(n+1)/a(n)

%e -- ---- -----------

%e 1 1 6

%e 2 6 0.666666...

%e 3 4 6

%e 4 24 0.625

%e 5 15 0.6

%e 6 9 6

%e 7 54 0.611111...

%e 8 33 0.060606...

%e 9 2 6

%e 10 12 0.666666...

%e 11 8 0.625

%e 12 5 0.6

%Y See A328752 for similar sequences.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Oct 27 2019