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

1,2

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