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

0,1

Comments

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

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

Links

Table of n, a(n) for n=0..50.

Formula

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

Example

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;
...

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 *)

Prog

(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

Crossrefs

See A004082 for another version.

As a function, this is the inverse of A067099.

Sequence in context: A078382 A075651 A091277 * A136484 A263621 A137039

Adjacent sequences: A277687 A277688 A277689 * A277691 A277692 A277693

Keyword

nonn

Author

John D. Dixon, Oct 26 2016

Extensions

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

Status

approved