Pi/8 - sqrt(2)/4.
3, 9, 1, 4, 5, 6, 9, 1, 1, 0, 5, 4, 5, 0, 3, 9, 2, 6, 0, 7, 4, 0, 8, 2, 4, 1, 8, 5, 7, 5, 1, 3, 3, 4, 0, 8, 8, 2, 2, 2, 8, 2, 0, 6, 0, 7, 7, 6, 5, 1, 2, 0, 9, 3, 2, 7, 6, 9, 8, 1, 3, 9, 5, 4, 0, 7, 9, 3, 9, 3, 1, 1, 7, 0, 2, 4, 9, 3, 6, 5, 1, 1, 5, 9, 0, 7, 4, 6, 9, 5, 8, 5, 8, 5, 4, 2, 4, 0, 3, 1, 4, 0, 1, 5, 0
-1
When an octagon is inscibed in a unit circle, this is the area of one of the eight segments of the circle not in the octagon.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Eric W. Weisstein, Circular segment
Wikipedia, Circular segment
This is Pi/n - sqrt((p^2+q^2)*((p-1)^2+q^2)), where p = (1 + cos(2*Pi/n))/2 and q = sin(2*Pi/n)/2 for n=8.
The number is 0.03914569110545039260740824185751334088222820607765….
(Mma) RealDigits[Pi/8 - Sqrt[2]/4, 10, 105][[1]]
Cf. S000236, S000237, S000238, S000243-S000249, S000250, S000251.
nonn,cons
T. D. Noe, Sep 05 2014