Pi/5 - sqrt((5 + sqrt(5))/32).
1, 5, 2, 7, 9, 0, 2, 7, 2, 5, 7, 0, 3, 8, 1, 8, 6, 1, 6, 3, 4, 3, 0, 9, 0, 0, 9, 9, 6, 6, 2, 0, 9, 5, 0, 5, 1, 3, 6, 5, 8, 4, 5, 6, 2, 8, 1, 2, 1, 4, 6, 0, 5, 2, 9, 7, 1, 3, 3, 6, 0, 9, 6, 2, 4, 6, 4, 8, 6, 6, 9, 6, 2, 1, 4, 6, 4, 5, 0, 4, 8, 8, 6, 6, 2, 1, 0, 5, 5, 9, 5, 8, 3, 0, 1, 7, 7, 2, 2, 7, 5, 8, 4, 7, 9, 7, 5, 8, 5
0
When a pentagon is inscibed in a unit circle, this is the area of one of the five segments of the circle not in the pentagon.
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=5.
The number is 0.1527902725703818616343090099662095051365845628….
(Mma) RealDigits[Pi/5 - Sqrt[(5 + Sqrt[5])/32], 10, 109][[1]]
Cf. S000236, S000237, S000238, S000244-S000249.
nonn,cons
T. D. Noe, Sep 04 2014