A121501: 

 Positions n of A121500 where the minimal relative error 

 E(n, A121500(n)):=|(F(n,A121500(n))-Pi)|/Pi, with

 F(n,m):= ((n/2)*sin(2*Pi/n) + m*tan(Pi/m))/2, for m=3..infinity, decreases.

 This error in approximating Pi is associated with the polygon problem described 

 in  A121500.

 The strictly decreasing sequence of relative errors in the circle area approximation by 

 the arithmetic mean of the areas of an inscribed regular n-gon and a circumscribed regular A121500(n)-gon 

(which leads to  minimal relative error for given n) is, with offset 1: 


 [0.3374167892e-1, 0.1503313669e-1, 0.8339154941e-2, 0.1487053500e-2, 0.6442095232e-3, 0.5089502881e-3, 

 0.4407098715e-3, 0.4391346825e-3, 0.1260185390e-3, 0.1471374482e-4, 0.1022126213e-4, 0.6477506798e-5, 

 0.1158382305e-5, 0.5288541810e-6, 0.4272545896e-6, 0.3733391943e-6, 0.3725372412e-6,...]


 Two examples:  
  
  i) The 4th value 0.1487053500e-2 = 0.001487053500, belongs to n = A121501(4)=8. Because A121500(8)=6, this 
                            
  is the minimal relative error for row n=8, namely E(8,6) (inscribed 8-gon, circumscribed 6-gon).

  ii) The 6th value 0.0005089502881, belongs to n = A121501(6)=14. Because A121500(14)=10 this 

  minmal relative error is the one for row n=14, namely  E(14,10) (inscribed 14-gon, circumscribed 10-gon).


 The list of [n,m] pairs leading to the above minimal errors E(n,m) when going down the rows n are:

 [[3, 3], [5, 4], [6, 5], [8, 6], [11, 8], [14, 10], [15, 11], [17, 12], [18, 13], [21, 15], [31, 22], [38, 27], 

  [48, 34], [65, 46], [82, 58], [89, 63], [99, 70],...]
  

 The corresponding m values are given as A121502.
 
  

################################################## e.o.f. #########################################################