login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Rounded down ratio of a minimum intersection area with a unit circle area in n-symmetrical unit circles intersect in a single point.
1

%I #18 Aug 18 2023 23:51:40

%S 17,5,77,17,210,40,445,77,812,133,1339,210,2056,313,2991,445,4175,610,

%T 5636,812,7403,1054,9506,1339,11973,1672,14835,2056,18120,2494,21856,

%U 2991,26075,3550,30804,4175,36073,4869

%N Rounded down ratio of a minimum intersection area with a unit circle area in n-symmetrical unit circles intersect in a single point.

%C Refer to construction rule in article "Circle-Circle Intersection" in MathWorld.

%C For n > 4, the intersected areas appearing at many sizes. In this case the minimum areas are considered. See illustration in links.

%H Kival Ngaokrajang, <a href="/A243933/a243933.pdf">Illustration of initial terms</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Circle-CircleIntersection.html">Circle-Circle Intersection</a>

%F For n > 2, a(n) = floor(Pi/area), where area = 2*arccos(cd/2) - (1/2)*cd*sqrt(4-cd^2), cd = 2*sin(((ang*360/n)*Pi/180)/2), ang = floor((n-1)/2).

%o (PARI) {for (n=3, 100, ang=floor((n-1)/2); cd=2*sin(((ang*360/n)*Pi/180)/2); area=2*acos(cd/2)-(1/2)*cd*(4-cd^2)^(1/2); print1(floor(Pi/area),", "))}

%K nonn

%O 3,1

%A _Kival Ngaokrajang_, Jun 15 2014