The On-Line Encyclopedia of Integer Sequences (OEIS)

The OEIS is supported by the many generous donors to the OEIS Foundation.

Revision History for A338643

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

Cycle lengths arising from interpreting sequence prefixes as graph node offsets.
(history; published version)

#16 by Susanna Cuyler at Fri Apr 23 20:53:14 EDT 2021

STATUS

proposed

approved

#15 by Rémy Sigrist at Fri Apr 23 11:04:21 EDT 2021

STATUS

editing

proposed

#14 by Rémy Sigrist at Fri Apr 23 11:03:13 EDT 2021

LINKS

Rémy Sigrist, <a href="/A338643/b338643.txt">Table of n, a(n) for n = 1..50000</a>

Rémy Sigrist, <a href="/A338643/a338643.txt">C program for A338643</a>

PROG

(C) See Links section.

STATUS

approved

editing

Discussion

Fri Apr 23

11:04

Rémy Sigrist: added b-file + program; the b-file is bigger than usual to show graphical features

#13 by Joerg Arndt at Fri Apr 23 01:18:57 EDT 2021

STATUS

reviewed

approved

#12 by Rémy Sigrist at Fri Apr 23 00:44:21 EDT 2021

STATUS

proposed

reviewed

#11 by Matthew Malone at Wed Apr 21 23:09:17 EDT 2021

STATUS

editing

proposed

Discussion

Wed Apr 21

23:18

Jon E. Schoenfield: Thanks!

Thu Apr 22

00:40

Rémy Sigrist: interesting sequence, with a nice graph; could you check a(44)?

02:06

Matthew Malone: For prefix a(1..43), I count:
a(1) = 1 -> a(2) = 1 -> a(3) = 2 -> a(5) = 3 -> a(8)* = 4 -> a(12) = 5 -> a(17) = 6 -> a(23) = 7 -> a(30) = 8 -> a(38) = 9 -> a(4) = 2 -> a(6) = 2 -> a(8)* which was visited 8 steps back, for an a(44) of 8. Have I missed something?

12:03

Rémy Sigrist: @Matthew: you're right, I was starting from position n-1 instead of position 1; the data matched except for n=44.

12:14

Matthew Malone: Starting from n-1 might be an interesting variation. There are lots of variations to explore within the framework of interpreting a sequence prefix as a directed graph.

#10 by Matthew Malone at Wed Apr 21 23:08:36 EDT 2021

NAME

Cycle lengths arising from interpreting sequence prefixes as graph node offsets.

STATUS

proposed

editing

#9 by Matthew Malone at Wed Apr 21 21:10:48 EDT 2021

STATUS

editing

proposed

Discussion

Wed Apr 21

21:38

Jon E. Schoenfield: The Name needs to end with a period.

#8 by Matthew Malone at Wed Apr 21 21:09:59 EDT 2021

EXAMPLE

Start with a(1) = 1. Treat a(1) = 1 as a node pointing 1 space ahead which, wrapping around the end of the length-1 prefix, points to itself. This is graph has a cycle length of 1, so a(2) = 1.

Now a(1..2) = [1, 1]. a(1) = 1 points 1 space ahead to a(2) and a(2) = 1 points 1 space ahead and wraps around to a(1), which is completing a cycle of length 2 so a(3) = 2.

#7 by Matthew Malone at Wed Apr 21 21:06:53 EDT 2021

EXAMPLE

Start with a(1) = 1. Treat 1 as a node pointing one 1 space ahead which, wrapping around the end of the length-1 prefix, points to itself. This is a cycle length of 1, so a(2) = 1.

Now a(1..2) = [1, 1]. a(1) = 1 points one 1 space ahead to a(2) and a(2) = 1 points 1 space ahead and wraps around to a(1), which is a cycle of length 2 so a(3) = 2.