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

Author

Rémy Sigrist, Jul 01 2020

Keywords

• nonn

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.

Examples

			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
		

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

Crossrefs

See A335944 for a similar sequence.

Cf. A000010, A057979, A088177.

Programs

PARI

See Links section.