

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.


2



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
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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



