A277690 Smallest possible number of sides of a regular polygon with unit sides and circumradius at least n.

3, 6, 13, 19, 26, 32, 38, 44, 51, 57, 63, 70, 76, 82, 88, 95, 101, 107, 114, 120, 126, 132, 139, 145, 151, 158, 164, 170, 176, 183, 189, 195, 202, 208, 214, 220, 227, 233, 239, 246, 252, 258, 264, 271, 277, 283, 290, 296, 302, 308, 315

Offset: 0

Author

John D. Dixon, Oct 26 2016

Keywords

• nonn

Comments

The average difference between terms in the sequence approaches 2*Pi.

Limit_{n -> oo} d/dn (Pi / arcsin(1/2n)) = 2*Pi.

Examples

			a(0) = 3, since this is the smallest number of sides a regular polygon may have;
a(1) = ceiling( Pi / arcsin(1/2) ) = ceiling( Pi/(Pi/6) ) = 6;
a(2) = ceiling( Pi / arcsin(1/4) ) = ceiling( Pi/(0.2526...) ) = 13;
...
		

Crossrefs

See A004082 for another version.

As a function, this is the inverse of A067099.

Programs

Mathematica

Table[If[n == 0, 3, Ceiling[Pi/ArcSin[1/(2 n)]]], {n, 0, 50}] (* Michael De Vlieger, Oct 28 2016 *) (* corrected on Aug 28 2023 by John D. Dixon *)

PARI

a(n) = if (n==0, 3, ceil(Pi/asin(1/(2*n)))); \\ Michel Marcus, Oct 28 2016; corrected Jun 13 2022 \\ corrected again on Aug 28 2023 by John D. Dixon

Formula

a(n) = ceiling( Pi / arcsin(1/(2*n)) ).

Extensions

First term and definition corrected by John D. Dixon, Aug 28 2023