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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. 2

%I

%S 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 10,11,12,11,10,11,10,11,12,11,12,13,13,13,13,11,12,11,13,15,13,13,13,

%U 13,14,15,14,17,13,13,13,15,14,17,14,15,14,17,15,17

%N 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 For any k > 0, k appears A000010(k) times.

%H Rémy Sigrist, <a href="/A335944/b335944.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A335944/a335944.png">Scatterplot of (n, frac(n/a(n))) for n = 1..50000</a>

%e The first terms, alongside the fractional part of n/a(n), are:

%e n a(n) frac(n/a(n))

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

%e 1 1 0

%e 2 3 2/3

%e 3 2 1/2

%e 4 3 1/3

%e 5 4 1/4

%e 6 5 1/5

%e 7 4 3/4

%e 8 5 3/5

%e 9 5 4/5

%e 10 7 3/7

%o (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 See A335943 for a similar sequence.

%Y Cf. A000010.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jul 01 2020

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Last modified January 30 19:55 EST 2023. Contains 359947 sequences. (Running on oeis4.)