A346128 Numbers m such that no self-avoiding walk that can make turns from the set 0, +-Pi/4, +-Pi/2, +-3*Pi/4, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

1, 2, 4, 5, 7, 8, 9, 11, 12, 13, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38

Offset

1,2

Comments

Closed walks (see A316198) are allowed, but except for the closed square-shaped walk of length 4 that fits into the same smallest enclosing circle as the smallest open walk of this length, no other closed walk that fits into a smaller enclosing circle than any open walk of the same length is known.

Links

Table of n, a(n) for n=1..31.

Hugo Pfoertner, Examples of paths of maximum length.

Example

See link for illustrations of terms corresponding to diameters D < 3.83.

Crossrefs

Cf. A127399, A127400, A127401, A306178, A316198.

Cf. A346123-A346132 similar to this sequence with other sets of turning angles.

Sequence in context: A184008 A183862 A254058 * A276220 A288204 A047381

Adjacent sequences: A346125 A346126 A346127 * A346129 A346130 A346131

Keyword

nonn,walk,more

Author

Hugo Pfoertner and Markus Sigg, Aug 01 2021

Status

approved