%I A121501
%S A121501 3,5,6,8,11,14,15,17,18,21,31,38,48,65,82,89,99,106,123,181,222,280,379,
%T A121501 478,519,577,618,717
%N A121501 Positions n of A121500 where the minimal relative error associated with 
               the polygon problem described there decreases.
%C A121501 The minimal relative errors for the unit circle area approximation by 
               the arithmetic mean of areas of an inscribed regular n-gon and a 
               circumscribed regular A121500(n)-gon decrease (strictly) for these 
               n=a(k) values. This results from a minimization, first within row 
               n and then along the rows n of the matrix E(n,m) defined below.
%H A121501 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A121501.text">
               Sequence of decreasing relative errors and more.</a>
%F A121501 a(k) is such that E(a(k),A121500(a(k)) < min(E(n,A121500(n)),n=3..a(k)-1), 
               k>=2, a(1):=3, with the relative error E(n,m):= abs(F(n,m)-Pi))/Pi 
               and F(n,m):= (Fin(n)+Fout(m))/2, where Fin(n):=(n/2)*sin(2*Pi/ n) 
               and Fout(m):= m*tan(Pi/m).
%e A121501 k=4, a(4)=8, m:= A121500(8)= 6. The relative error associated with
%e A121501 F(n=8,m=6) is the smallest among those with values n=3,..,8.
%e A121501 (n,m) pairs (a(k),A121500(a(k)),k=1..7: [3, 3], [5, 4], [6, 5], [8,
%e A121501 6], [11, 8], [14, 10], [15, 11],...
%Y A121501 Cf. A121502 (corresponding A121500(a(k)) numbers).
%Y A121501 Sequence in context: A154111 A047444 A160734 this_sequence A157017 A062832 
               A089085
%Y A121501 Adjacent sequences: A121498 A121499 A121500 this_sequence A121502 A121503 
               A121504
%K A121501 nonn,more
%O A121501 1,1
%A A121501 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 
               2006