format long

T = 1.047197551196598
for i= 1:6 % works fine with 6 iterations
   x = atan(10^(-i+1))
n = floor(T/x)
y(i) = n
m(i) = x
T = T - n*x

end
% let A be a 1x8 matrix of the values y(i) from i=1 to i=8
A = [ 1,     2,     6,     2,     4, 6]
% let B be a 1x8 matrix of the values of m(i) for i=1 to i=8
B = [0.785398163397448,   0.099668652491162,   0.009999666686665,   0.000999999666667, 0.000099999999667, 0.000010000000000]
% check to see if our found integers multiplied respective basis work
dot(A,B)