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