A387606 Decimal expansion of the area of the half-plane of the positive ordinates bounded between the curves of equations x^2 + y^2 = 1 and y = x^2.

1, 0, 6, 6, 5, 1, 2, 9, 8, 4, 8, 8, 7, 9, 2, 9, 9, 2, 3, 5, 2, 1, 6, 0, 4, 7, 5, 4, 2, 9, 3, 4, 6, 9, 5, 7, 5, 4, 9, 5, 2, 5, 6, 5, 5, 5, 6, 2, 9, 0, 6, 2, 7, 3, 7, 9, 7, 3, 2, 4, 4, 5, 9, 0, 8, 2, 9, 3, 0, 1, 0, 5, 6, 4, 0, 1, 9, 6, 4, 2, 5, 0, 3, 1, 2, 2, 6, 7, 6, 9, 0, 1, 1, 1, 4, 6, 1, 4, 3, 9

Offset

1,3

Links

Table of n, a(n) for n=1..100.

Index entries for transcendental numbers.

Formula

Equals Integral_{x=-c,c} (sqrt(1-x^2) - x^2) dx, where c = sqrt((sqrt(5)-1)/2) = A197762.

Equals sqrt(sqrt(5)-2)/3 + arcsin(sqrt((sqrt(5)-1)/2)).

Example

1.0665129848879299235216047542934695754952565556...

Mathematica

RealDigits[Sqrt[Sqrt[5]-2]/3+ArcSin[Sqrt[(Sqrt[5]-1)/2]], 10, 100][[1]]

Crossrefs

Cf. A195692, A197762.

Sequence in context: A104225 A374755 A292179 * A255823 A011188 A246184

Adjacent sequences: A387603 A387604 A387605 * A387607 A387608 A387609

Keyword

nonn,cons

Author

Stefano Spezia, Sep 03 2025

Status

approved