A342236 a(n) is the smallest m such that a regular m-gon with all diagonals drawn contains a cell with n sides, as in A342222, but for odd m the central m-sided polygon is not considered. Otherwise a(n) = -1 if no such m exists.

4, 6, 7, 9, 15, 13, 35, 29, 29, 40, 93, 43, 399, 212

Offset

3,1

Comments

An m-gon with an odd number of sides contains a central cell with m sides by its construction, and it will be the m-gon with the fewest possible sides to do so. See A342222 for a proof. This sequence lists the smallest m-sided polygon to contain an n-sided cell where this central cell is not considered for odd m.

See A342222 for other images of the m-sided polygons.

a(17) is presently unknown, but if a(17) > 0 it is greater than 765.

Links

Table of n, a(n) for n=3..16.

Scott R. Shannon, Image for a(3) = 4.

Scott R. Shannon, Image for a(9) = 35.

Scott R. Shannon, Image for a(13) = 93.

Crossrefs

Cf. A342222, A007678, A331450, A331451, A007569, A135565.

See also A341729 and A341730 for the maximum number of sides in any cell.

Sequence in context: A010448 A005621 A140468 * A349549 A010418 A243193

Adjacent sequences: A342233 A342234 A342235 * A342237 A342238 A342239

Keyword

nonn,more

Author

Scott R. Shannon and N. J. A. Sloane, Mar 06 2021

Extensions

a(15)-a(16) added by Scott R. Shannon, Mar 15 2021

Minimum value for a(17) updated by Scott R. Shannon, Mar 21 2021

Minimum value for a(17) updated by Scott R. Shannon, Nov 30 2021

Status

approved