

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



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, 10, 11, 12, 11, 10, 11, 10, 11, 12, 11, 12, 13, 13, 13, 13, 11, 12, 11, 13, 15, 13, 13, 13, 13, 14, 15, 14, 17, 13, 13, 13, 15, 14, 17, 14, 15, 14, 17, 15, 17
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OFFSET

1,2


COMMENTS

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


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of (n, frac(n/a(n))) for n = 1..50000


EXAMPLE

The first terms, alongside the fractional part of n/a(n), are:
n a(n) frac(n/a(n))
  
1 1 0
2 3 2/3
3 2 1/2
4 3 1/3
5 4 1/4
6 5 1/5
7 4 3/4
8 5 3/5
9 5 4/5
10 7 3/7


PROG

(PARI) ff = []; for (n=1, 72, for (v=1, oo, if (!setsearch(ff, f=frac(n/v)), print1 (v ", "); ff=setunion(ff, [f]); break)))


CROSSREFS

See A335943 for a similar sequence.
Cf. A000010.
Sequence in context: A091563 A161985 A292787 * A035366 A114751 A211947
Adjacent sequences: A335941 A335942 A335943 * A335945 A335946 A335947


KEYWORD

nonn


AUTHOR

Rémy Sigrist, Jul 01 2020


STATUS

approved



