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.

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

Offset: 1

Author

Rémy Sigrist, Jul 01 2020

Keywords

• nonn

Comments

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

Examples

			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
		

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

Crossrefs

See A335943 for a similar sequence.

Cf. A000010.

Programs

PARI

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