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A244093 Rounded down ratio of area of a unit circle and a circle inscribed in any of the n triangles composing a regular n-gon 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 (list; graph; refs; listen; history; text; internal format)
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 n-gon. - Wolfdieter Lang, Jun 30 2014

PROG

(PARI)

{

  for (n=3, 100,

     c=2*sin(Pi/n);

     s=(2+c)/2;

     r=sqrt(((s-1)^2*(s-c))/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

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Last modified June 2 10:57 EDT 2020. Contains 334771 sequences. (Running on oeis4.)