A335943 Lexicographically earliest sequence of positive terms such that for any distinct m and n, the fractional parts of a(m)/a(m+1) and of a(n)/a(n+1) are distinct.

1, 1, 2, 3, 4, 3, 5, 4, 5, 6, 5, 7, 5, 8, 7, 6, 7, 8, 9, 7, 9, 8, 11, 7, 10, 7, 11, 8, 13, 9, 10, 9, 11, 9, 13, 10, 11, 10, 13, 11, 12, 11, 13, 12, 13, 14, 9, 14, 11, 14, 13, 15, 11, 15, 13, 16, 11, 16, 13, 17, 11, 17, 12, 17, 13, 18, 13, 19, 12, 19, 13, 20

Offset

1,3

Comments

For any k > 1, k appears up to A000010(k) times.

This sequence has similarities with A057979 and A088177, where we consider the ratio and the product of consecutive terms, respectively.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

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

Rémy Sigrist, Colored scatterplot of (numerator(frac(a(n)/a(n+1))), denominator(frac(a(n)/a(n+1)))) for n = 1..232289 (where the hue is function of n)

Rémy Sigrist, PARI program for A335943

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A335944 for a similar sequence.

Cf. A000010, A057979, A088177.

Sequence in context: A075850 A327565 A054437 * A287821 A341830 A357714

Adjacent sequences: A335940 A335941 A335942 * A335944 A335945 A335946

Keyword

nonn

Author

Rémy Sigrist, Jul 01 2020

Status

approved