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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 06:09 EST 2022. Contains 358454 sequences. (Running on oeis4.)