Pi/6 - sqrt(3)/4.
9, 0, 5, 8, 6, 0, 7, 3, 7, 0, 6, 0, 7, 9, 5, 4, 9, 6, 9, 5, 2, 4, 5, 6, 4, 5, 1, 7, 0, 1, 1, 5, 7, 2, 2, 2, 9, 7, 1, 6, 0, 2, 5, 3, 1, 0, 9, 9, 2, 2, 4, 7, 9, 8, 1, 5, 2, 0, 5, 6, 8, 7, 1, 8, 8, 3, 1, 9, 4, 8, 0, 1, 5, 3, 8, 3, 4, 8, 2, 3, 8, 3, 4, 3, 8, 5, 9, 2, 4, 2, 0, 1, 0, 4, 0, 7, 0, 0, 7, 4, 4, 7, 8, 4, 8
-1
When a 30-60-90 triangle is inscibed in a unit half-circle (having diameter 2), this is the area of smaller circular segment.
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=6.
The number is 0.090586073706079549695245645170115722297….
(Mma) RealDigits[Pi/6 - Sqrt[3]/4, 10, 105][[1]]
Cf. S000236 (circular segment for square), S000237 (larger circular segment), S000243-S000249.
nonn,cons
T. D. Noe, Sep 02 2014