%I #13 Aug 18 2023 23:36:37
%S 1,3,4,6,7,9,11,12,14,15,17,18,20,21,23,25,26,28,29,31,32,34,36,37,39,
%T 40,42,43,45,47,48,50,51,53,54,56,58,59,61,62,64,65,67,69,70,72,73,75,
%U 76,78,80,81,83,84,86,87,89,91,92,94,95,97,98,100,102,103
%N Rounded down ratio of a lune area and a unit circle one, the lune is bounded by two unit circles whose centers are separated by a distance 1/n.
%C It seems to be for n >= 10 the first difference will be periodic of {1, 2, 1, 2, 1, 2, 2}.
%H Kival Ngaokrajang, <a href="/A243989/a243989.pdf">Illustration of initial terms</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Lune.html">Lune</a>
%F a(n) = floor(Pi/area) where area = 2*d + k1 - k2, d = (1/4)*(c^2*(2+c)*(2-c))^(1/2), k1 = arccos(-c^2/(2*c)), k2 = arccos(c^2/(2*c)).
%F Empirical g.f.: x*(x^14-x^13+2*x^6+2*x^5+x^4+2*x^3+x^2+2*x+1) / ((x-1)^2*(x^6+x^5+x^4+x^3+x^2+x+1)). - _Colin Barker_, Jun 17 2014
%o (PARI)
%o {
%o for (n=1, 100, c=1/n;
%o d = (1/4)*(c^2*(2+c)*(2-c))^(1/2);
%o k1 = acos(-c^2/(2*c));
%o k2 = acos(c^2/(2*c));
%o area = 2*d+k1-k2;
%o print1(floor(Pi/area),", ")
%o )
%o }
%K nonn
%O 1,2
%A _Kival Ngaokrajang_, Jun 17 2014