The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A355616 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A355616

a(n) is the number of distinct lengths between consecutive points of the Farey sequence of order n.
(history; published version)

#31 by Alois P. Heinz at Sat Jul 16 12:04:18 EDT 2022

STATUS

proposed

approved

#30 by Jean-François Alcover at Sat Jul 16 12:02:23 EDT 2022

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editing

proposed

#29 by Jean-François Alcover at Sat Jul 16 12:02:13 EDT 2022

MATHEMATICA

a[n_] := FareySequence[n] // Differences // Union // Length;

Table[a[n], {n, 1, 70}] (* Jean-François Alcover, Jul 16 2022 *)

STATUS

approved

editing

#28 by Joerg Arndt at Sat Jul 16 07:13:46 EDT 2022

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reviewed

approved

#27 by Kevin Ryde at Sat Jul 16 05:20:03 EDT 2022

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proposed

reviewed

Discussion

Sat Jul 16

05:31

Michel Marcus: I preferred Kevin presentation

#26 by Kevin Ryde at Sat Jul 16 05:19:43 EDT 2022

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editing

proposed

#25 by Kevin Ryde at Sat Jul 16 05:16:44 EDT 2022

EXAMPLE

For n=4, the Farey sequence of order 4, its differences between consecutive points, and the resulting a(4) = 3 distinct differences are

Farey 0, 1/4, 1/3, 1/2, 2/3, 3/4, 1

differences 1/4, 1/12, 1/6, 1/6, 1/12, 1/4

3 distinct differences: 1/12, 1/6, 1/4

STATUS

reviewed

editing

Discussion

Sat Jul 16

05:19

Kevin Ryde: I don't want to double up examples.  Take away mine.

#24 by Michel Marcus at Sat Jul 16 02:10:42 EDT 2022

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proposed

reviewed

#23 by Kevin Ryde at Fri Jul 15 19:30:50 EDT 2022

STATUS

editing

proposed

Discussion

Fri Jul 15

19:33

Kevin Ryde: (Apart from that you're about right I think.)

#22 by Kevin Ryde at Fri Jul 15 19:28:14 EDT 2022

COMMENTS

The Farey sequence of order n (row n of A006842/A006843) is the set of points x/y on the unit line where 0 <= x 1 <= y <= n and 1 0 <= x <= y <= n.

Discussion

Fri Jul 15

19:30

Kevin Ryde: This is some bits I thought.  The example aims for a little bit visual, since you're talking about points etc.  You can choose which way to keep (or merge!).