cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A349421 Numbers k such that a regular k-gon, when its vertices are connected by infinite lines, creates polygons outside the k-gon with more sides than any polygon inside the k-gon, excluding the central k-sided polygon for odd values of k.

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%I A349421 #25 Jun 25 2022 12:54:26
%S A349421 14,19,29,32,33,39,52
%N A349421 Numbers k such that a regular k-gon, when its vertices are connected by infinite lines, creates polygons outside the k-gon with more sides than any polygon inside the k-gon, excluding the central k-sided polygon for odd values of k.
%C A349421 As a regular k-gon with an odd number of sides always creates a k-sided polygon at the center of the k-gon when its vertices are connected by lines (see A342222), this polygon is excluded when considering the polygons inside the k-gon with the maximum number of sides.
%C A349421 If the next term exists it is greater than 100.
%H A349421 Scott R. Shannon, <a href="/A349421/a349421.gif">Image for the 32-gon</a>.
%e A349421 14 is a term as when a regular 14-gon's vertices are connected by infinite lines fourteen 6-gons are created outside the vertices while the maximum-sided polygons created inside are 5-gons. See the 14-gon image in A344857.
%e A349421 19 is a term as when a regular 19-gon's vertices are connected by infinite lines nineteen 10-gons are created outside the vertices while the maximum-sided polygons created inside, excluding the central 19-gon, are 8-gons. See the 19-gon image in A344857.
%e A349421 32 is a term as when a regular 32-gon's vertices are connected by infinite lines sixty-four 8-gons are created outside the vertices while the maximum-sided polygons created inside are 7-gons. See the linked image.
%Y A349421 Cf. A344938, A344857, A344311, A007678, A342222.
%K A349421 nonn,more,hard
%O A349421 1,1
%A A349421 _Scott R. Shannon_, Nov 17 2021