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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 "7".
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%I #8 Oct 29 2019 04:40:13

%S 1,7,5,35,25,18,13,10,70,49,36,26,2,14,11,8,6,42,3,21,15,105,74,52,4,

%T 28,20,140,98,69,50,37,27,19,133,94,66,47,33,24,17,12,9,63,45,32,23,

%U 161,113,80,56,40,29,22,16,112,79,57,41,30,210,147,103,73,53

%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 "7".

%C In other words, for any n > 0, we have an integer k such that floor(10^k * a(n+1)/a(n)) = 7.

%H Rémy Sigrist, <a href="/A328758/b328758.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 7

%e 2 7 0.714285...

%e 3 5 7

%e 4 35 0.714285...

%e 5 25 0.72

%e 6 18 0.722222...

%e 7 13 0.769230...

%e 8 10 7

%e 9 70 0.7

%e 10 49 0.734693...

%e 11 36 0.722222...

%e 12 26 0.076923...

%Y See A328752 for similar sequences.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Oct 27 2019