

A244093


Rounded down ratio of area of a unit circle and a circle inscribed in any of the n triangles composing a regular ngon which is circumscribed by a unit circle.


4



18, 11, 11, 12, 13, 15, 17, 19, 22, 25, 28, 31, 35, 39, 42, 47, 51, 56, 60, 65, 70, 76, 81, 87, 93, 99, 106, 112, 119, 126, 133, 141, 148, 156, 164, 173, 181, 190, 198, 207, 217, 226, 236, 246, 256, 266, 276, 287, 298, 309, 320, 332, 343, 355, 367, 380, 392, 405, 418, 431, 444
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OFFSET

3,1


COMMENTS

The minimum ratio occurs at n = 5.


LINKS

Table of n, a(n) for n=3..63.
Kival Ngaokrajang, Illustration of initial terms


FORMULA

a(n) = floor(Pi/area(n)) where area = Pi*r(n)^2, r(n) = (s(n)/2)*sqrt((2  s(n))/(2 + s(n))), with s(n) = 2*sin(Pi/n) which is the side length (length unit 1) of the regular n gon. [rewritten by Wolfdieter Lang, Jun 30 2014 and Jul 02 2014]
a(n) = floor(1/r(n)^2) with r(n) = S(n)*(1 + C(n)  S(n))/(1 + C(n) + S(n)) with S(n) = s(n)/2 and C(n) = cos(Pi/n). 2*C(n) is the ratio of the length of the smallest diagonal and the side length s(n) in the regular ngon.  Wolfdieter Lang, Jun 30 2014


PROG

(PARI)
{
for (n=3, 100,
c=2*sin(Pi/n);
s=(2+c)/2;
r=sqrt(((s1)^2*(sc))/s);
area=Pi*r^2;
a=floor(Pi/area);
print1(a, ", ")
)
}


CROSSREFS

Cf. A244094, A244096.
Sequence in context: A089517 A290345 A035616 * A195926 A195929 A247604
Adjacent sequences: A244090 A244091 A244092 * A244094 A244095 A244096


KEYWORD

nonn


AUTHOR

Kival Ngaokrajang, Jun 20 2014


STATUS

approved



