cp's OEIS Frontend

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

%I A277690 #40 Sep 26 2023 20:30:19
%S A277690 3,6,13,19,26,32,38,44,51,57,63,70,76,82,88,95,101,107,114,120,126,
%T A277690 132,139,145,151,158,164,170,176,183,189,195,202,208,214,220,227,233,
%U A277690 239,246,252,258,264,271,277,283,290,296,302,308,315
%N A277690 Smallest possible number of sides of a regular polygon with unit sides and circumradius at least n.
%C A277690 The average difference between terms in the sequence approaches 2*Pi.
%C A277690 Limit_{n -> oo} d/dn (Pi / arcsin(1/2n)) = 2*Pi.
%F A277690 a(n) = ceiling( Pi / arcsin(1/(2*n)) ).
%e A277690 a(0) = 3, since this is the smallest number of sides a regular polygon may have;
%e A277690 a(1) = ceiling( Pi / arcsin(1/2) ) = ceiling( Pi/(Pi/6) ) = 6;
%e A277690 a(2) = ceiling( Pi / arcsin(1/4) ) = ceiling( Pi/(0.2526...) ) = 13;
%e A277690 ...
%t A277690 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_ *)
%o A277690 (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_
%Y A277690 See A004082 for another version.
%Y A277690 As a function, this is the inverse of A067099.
%K A277690 nonn
%O A277690 0,1
%A A277690 _John D. Dixon_, Oct 26 2016
%E A277690 First term and definition corrected by _John D. Dixon_, Aug 28 2023