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A335944 Lexicographically earliest sequence of positive integers such that for any distinct m and n, the fractional parts of m/a(m) and of n/a(n) are distinct.

%I A335944 #10 Jul 06 2020 02:21:21
%S A335944 1,3,2,3,4,5,4,5,5,7,6,5,6,9,7,7,8,7,7,7,8,9,8,11,9,9,8,9,9,11,10,11,
%T A335944 10,11,12,11,10,11,10,11,12,11,12,13,13,13,13,11,12,11,13,15,13,13,13,
%U A335944 13,14,15,14,17,13,13,13,15,14,17,14,15,14,17,15,17
%N A335944 Lexicographically earliest sequence of positive integers such that for any distinct m and n, the fractional parts of m/a(m) and of n/a(n) are distinct.
%C A335944 For any k > 0, k appears A000010(k) times.
%H A335944 Rémy Sigrist, <a href="/A335944/b335944.txt">Table of n, a(n) for n = 1..10000</a>
%H A335944 Rémy Sigrist, <a href="/A335944/a335944.png">Scatterplot of (n, frac(n/a(n))) for n = 1..50000</a>
%e A335944 The first terms, alongside the fractional part of n/a(n), are:
%e A335944   n   a(n)  frac(n/a(n))
%e A335944   --  ----  ------------
%e A335944    1     1       0
%e A335944    2     3      2/3
%e A335944    3     2      1/2
%e A335944    4     3      1/3
%e A335944    5     4      1/4
%e A335944    6     5      1/5
%e A335944    7     4      3/4
%e A335944    8     5      3/5
%e A335944    9     5      4/5
%e A335944   10     7      3/7
%o A335944 (PARI) ff = []; for (n=1, 72, for (v=1, oo, if (!setsearch(ff, f=frac(n/v)), print1 (v ", "); ff=setunion(ff, [f]); break)))
%Y A335944 See A335943 for a similar sequence.
%Y A335944 Cf. A000010.
%K A335944 nonn
%O A335944 1,2
%A A335944 _Rémy Sigrist_, Jul 01 2020