The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A346126

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

A346126

Numbers m such that no self-avoiding walk of length m + 1 on the hexagonal lattice fits into the smallest circle that can enclose a walk of length m.
(history; published version)

#11 by Hugo Pfoertner at Sun Aug 08 12:34:51 EDT 2021

STATUS

editing

approved

#10 by Hugo Pfoertner at Sun Aug 08 12:33:42 EDT 2021

EXAMPLE

See link for illustrations of terms corresponding to diameters D < 5.64= 8.

STATUS

approved

editing

Discussion

Sun Aug 08

12:34

Hugo Pfoertner: Limit for D updated in example.

#9 by Bruno Berselli at Sun Aug 08 12:18:37 EDT 2021

STATUS

proposed

approved

#8 by Hugo Pfoertner at Sun Aug 08 12:16:17 EDT 2021

STATUS

editing

proposed

#7 by Hugo Pfoertner at Sun Aug 08 12:16:03 EDT 2021

DATA

1, 3, 4, 7, 8, 9, 10, 12, 14, 15, 16, 19, 20, 22, 23, 24, 25, 27, 31, 32, 34, 37, 38, 39, 40, 42, 43, 44, 45, 48, 49, 55, 56, 57, 58, 60, 61

STATUS

approved

editing

#6 by Susanna Cuyler at Tue Aug 03 12:29:16 EDT 2021

STATUS

proposed

approved

#5 by Hugo Pfoertner at Tue Aug 03 05:02:54 EDT 2021

STATUS

editing

proposed

#4 by Hugo Pfoertner at Tue Aug 03 04:59:10 EDT 2021

CROSSREFS

Cf. A122226, A125852, A127399, A127400, A127401, A151541, A284869, A306176, A316196, A346123, A346124, A346125, A346132.

Cf. A346123 (similar to this sequence, but for honeycomb net), A346124 (ditto for square lattice).

Cf. A346125, A346127-A346132 (similar to this sequence, but with other sets of turning angles).

#3 by Hugo Pfoertner at Sat Jul 31 15:33:36 EDT 2021

CROSSREFS

Cf. A122226, A125852, A127399, A127400, A127401, A151541, A284869, A306176, A316196, A346123, A346124, A346125, A346132.

AUTHOR

Hugo Pfoertner, and _Markus Sigg_, Jul 31 2021

#2 by Hugo Pfoertner at Sat Jul 31 15:29:30 EDT 2021

NAME

allocated for Hugo PfoertnerNumbers m such that no self-avoiding walk of length m + 1 on the hexagonal lattice fits into the smallest circle that can enclose a walk of length m.

DATA

1, 3, 4, 7, 8, 9, 10, 12, 14, 15, 16, 19, 20, 22, 23, 24, 25, 27, 31, 32

OFFSET

1,2

COMMENTS

Open and closed walks are allowed. It is conjectured that all optimal paths are closed except for the trivial path of length 1. See the related conjecture in A122226.

LINKS

Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a346126.htm">Examples of paths of maximum length</a>.

EXAMPLE

See link for illustrations of terms corresponding to diameters D < 5.64.

CROSSREFS

Cf. A122226, A125852, A127399, A127400, A127401, A151541, A284869, A306176, A316196, A346123, A346124, A346132.

KEYWORD

allocated

nonn,walk,more

AUTHOR

Hugo Pfoertner, Jul 31 2021

STATUS

approved

editing