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

Author

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

Keywords

• nonn
• more

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

• 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.

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