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A335943 Lexicographically earliest sequence of positive terms such that for any distinct m and n, the fractional parts of a(m)/a(m+1) and of a(n)/a(n+1) are distinct.

%I A335943 #15 Jul 06 2020 02:21:24
%S A335943 1,1,2,3,4,3,5,4,5,6,5,7,5,8,7,6,7,8,9,7,9,8,11,7,10,7,11,8,13,9,10,9,
%T A335943 11,9,13,10,11,10,13,11,12,11,13,12,13,14,9,14,11,14,13,15,11,15,13,
%U A335943 16,11,16,13,17,11,17,12,17,13,18,13,19,12,19,13,20
%N A335943 Lexicographically earliest sequence of positive terms such that for any distinct m and n, the fractional parts of a(m)/a(m+1) and of a(n)/a(n+1) are distinct.
%C A335943 For any k > 1, k appears up to A000010(k) times.
%C A335943 This sequence has similarities with A057979 and A088177, where we consider the ratio and the product of consecutive terms, respectively.
%H A335943 Rémy Sigrist, <a href="/A335943/b335943.txt">Table of n, a(n) for n = 1..10000</a>
%H A335943 Rémy Sigrist, <a href="/A335943/a335943.png">Scatterplot of (n, frac(a(n)/a(n+1))) for n = 1..50000</a>
%H A335943 Rémy Sigrist, <a href="/A335943/a335943_1.png">Colored scatterplot of (numerator(frac(a(n)/a(n+1))), denominator(frac(a(n)/a(n+1)))) for n = 1..232289</a> (where the hue is function of n)
%H A335943 Rémy Sigrist, <a href="/A335943/a335943.gp.txt">PARI program for A335943</a>
%e A335943 The first terms, alongside the fractional part of a(n)/a(n+1), are:
%e A335943   n   a(n)  frac(a(n)/a(n+1))
%e A335943   --  ----  -----------------
%e A335943    1     1          0
%e A335943    2     1         1/2
%e A335943    3     2         2/3
%e A335943    4     3         3/4
%e A335943    5     4         1/3
%e A335943    6     3         3/5
%e A335943    7     5         1/4
%e A335943    8     4         4/5
%e A335943    9     5         5/6
%e A335943   10     6         1/5
%o A335943 (PARI) See Links section.
%Y A335943 See A335944 for a similar sequence.
%Y A335943 Cf. A000010, A057979, A088177.
%K A335943 nonn
%O A335943 1,3
%A A335943 _Rémy Sigrist_, Jul 01 2020